🔗 Problem

Problem: A rectangle has a length of 21m and a width of 37m. What is the perimeter of the rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides.

    Given:
    - Length of the rectangle is 21m
    - Width of the rectangle is 37m

    The formula for the perimeter of a rectangle is:
    Perimeter = 2 × (length + width)

    Calculation:
    Perimeter = 2 × (21m + 37m)
    Perimeter = 2 × 58m
    Perimeter = 116m

    Therefore, the perimeter of the rectangle is 116m.

    ### Answer: 116m

Expected answer: 116

Correct? Yes

🔗 Follow-up

Problem: Now consider that the length of the rectangle has changed to 4m while the width remains at 37m. What is the new perimeter of the rectangle?

Gemma 2B:

    Great! Let's solve this problem with the updated information.

    Given:
    - The new length of the rectangle is 4m
    - The width of the rectangle remains at 37m

    We will use the same formula for the perimeter of a rectangle:
    Perimeter = 2 × (length + width)

    Calculation:
    Perimeter = 2 × (4m + 37m)
    Perimeter = 2 × 41m
    Perimeter = 82m

    Therefore, with the new length of 4m and the width of 37m, the perimeter of the rectangle is now 82m.

    ### Answer: 82m

Expected answer: 82

Correct? Yes

🔗 Problem

Problem: A rectangular garden has a length of 50 feet and a width of 20 feet. What is the perimeter of the garden?

Gemma 2B:

    To find the perimeter of the rectangular garden, we need to add up the lengths of all four sides.

    Given:
    - Length of the garden = 50 feet
    - Width of the garden = 20 feet

    Step 1: Calculate the perimeter of the garden.
    Perimeter = 2 × (Length + Width)
    Perimeter = 2 × (50 feet + 20 feet)
    Perimeter = 2 × 70 feet
    Perimeter = 140 feet

    ### Answer: The perimeter of the garden is 140 feet.

Expected answer: 140

Correct? Yes

🔗 Follow-up

Problem: A landscaper plans to reduce the length of the rectangular garden to 15 feet while keeping the width the same. What will the new perimeter of the garden be?

Gemma 2B:

    Let's solve this problem step by step using the new length of the garden.

    Given:
    - New length of the garden = 15 feet
    - Width of the garden = 20 feet (unchanged)

    Step 1: Calculate the new perimeter of the garden.
    New Perimeter = 2 × (New Length + Width)
    New Perimeter = 2 × (15 feet + 20 feet)
    New Perimeter = 2 × 35 feet
    New Perimeter = 70 feet

    ### Answer: The new perimeter of the garden will be 70 feet.

Expected answer: 70

Correct? Yes

🔗 Problem

Problem: A rectangle has a width of 7m and a length of 26m. What is the area of this rectangle?

Gemma 2B:

    To find the area of a rectangle, we use the formula:

    Area = length × width

    Given:
    - The width of the rectangle is 7m.
    - The length of the rectangle is 26m.

    Calculation:
    Area = 26m × 7m = <<26*7=182>>182m²

    Therefore, the area of the rectangle is 182 square meters.

    ### Answer: 182m²

Expected answer: 182

Correct? Yes

🔗 Follow-up

Problem: The width of the rectangle stays the same at 7m, but the length extends by 9m to become 35m. What is the area of the rectangle now?

Gemma 2B:

    Great! Let's solve this problem step by step. We'll use the same formula for the area of a rectangle: Area = length × width.

    Given:
    - The width of the rectangle remains 7m.
    - The length of the rectangle is now 35m (extended by 9m from the previous 26m).

    Calculation:
    Area = 35m × 7m = <<35*7=245>>245m²

    Therefore, after extending the length by 9m, the new area of the rectangle is 245 square meters.

    ### Answer: 245m²

Expected answer: 245

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 50m and a width of 15m. What is its perimeter?

Gemma 2B:

    To find the perimeter of the rectangle, we need to use the formula:

    Perimeter of a rectangle = 2 × (length + width)

    Given:
    - Length of the rectangle = 50m
    - Width of the rectangle = 15m

    Now, let's calculate the perimeter:

    Perimeter = 2 × (50m + 15m)
    Perimeter = 2 × 65m
    Perimeter = 130m

    ### Answer: 130m

Expected answer: 130

Correct? Yes

🔗 Follow-up

Problem: The rectangle mentioned in the previous problem had its width reduced to 9m while the length remained the same. What is the new perimeter of the rectangle?

Gemma 2B:

    In this problem, we need to find the new perimeter of the rectangle after the width has been reduced to 9m, while the length remains the same at 50m.

    Given:
    - New width of the rectangle = 9m
    - Length of the rectangle = 50m (unchanged)

    Using the formula for the perimeter of a rectangle:

    Perimeter of a rectangle = 2 × (length + width)

    Let's calculate the new perimeter:

    New Perimeter = 2 × (50m + 9m)
    New Perimeter = 2 × 59m
    New Perimeter = 118m

    ### Answer: 118m

Expected answer: 118

Correct? Yes

🔗 Problem

Problem: A rectangular fence has a side length of 5m and another side of 19m. What is the total distance, in meters, around the fence (perimeter)?

Gemma 2B:

    To find the perimeter of a rectangle, we use the formula:

    Perimeter = 2 × (length + width)

    Given:
    - One side length of the rectangular fence is 5 meters.
    - The other side length of the rectangular fence is 19 meters.

    Calculation:
    Perimeter = 2 × (5 + 19)
    Perimeter = 2 × 24
    Perimeter = 48 meters

    ### Answer: 48 meters.

Expected answer: 48

Correct? Yes

🔗 Follow-up

Problem: The owner of the fence decided to extend the side that originally measured 19m to a new length of 36m, while the other side remains the same. After the extension, what will be the new total distance, in meters, around the fence (perimeter)?

Gemma 2B:

    Great! Let's solve this problem step by step. We'll use the same formula for the perimeter of a rectangle, but with the updated length.

    Given:
    - One side length of the rectangular fence remains 5 meters.
    - The other side length of the rectangular fence has been extended from 19 meters to 36 meters.

    Calculation:
    Perimeter = 2 × (length + width)
    Perimeter = 2 × (5 + 36)
    Perimeter = 2 × 41
    Perimeter = 82 meters

    ### Answer: 82 meters.

Expected answer: 82

Correct? Yes

🔗 Problem

Problem: A rectangle has sides of length 49m and 6m. What is the perimeter of the rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides.

    Given:
    - The length of one side is 49 meters.
    - The length of the other side is 6 meters.

    In a rectangle, opposite sides are equal in length. So, there are two sides with a length of 49 meters and two sides with a length of 6 meters.

    Perimeter = 2 × (length + width)
    Perimeter = 2 × (49 m + 6 m)
    Perimeter = 2 × 55 m
    Perimeter = 110 m

    ### Answer: 110 meters.

Expected answer: 110

Correct? Yes

🔗 Follow-up

Problem: Suppose we were mistaken in the original measurement, and one side of the rectangle was actually 17m instead of 49m. What would the new perimeter of the rectangle be?

Gemma 2B:

    Okay, let's recalculate the perimeter with the corrected length.

    Given:
    - The length of one side is 17 meters (instead of 49 meters).
    - The length of the other side is still 6 meters.

    In a rectangle, opposite sides are equal in length. So, there are two sides with a length of 17 meters and two sides with a length of 6 meters.

    Perimeter = 2 × (length + width)
    Perimeter = 2 × (17 m + 6 m)
    Perimeter = 2 × 23 m
    Perimeter = 46 m

    ### Answer: 46 meters.

Expected answer: 46

Correct? Yes

🔗 Problem

Problem: Joshua plans to lay a wire around his rectangular garden. If the garden is 7m wide and 26m long, how much wire will Joshua need to enclose the garden completely?

Gemma 2B:

    To solve this problem, let's follow these steps:

    1. Understand the shape of the garden:
       * The garden is rectangular.
       * It has a width of 7 meters and a length of 26 meters.

    2. Recall the formula for the perimeter of a rectangle:
       * Perimeter of a rectangle = 2 × (length + width)

    3. Plug in the values and calculate:
       * Perimeter = 2 × (26 m + 7 m)
       * Perimeter = 2 × 33 m
       * Perimeter = 66 m

    Therefore, Joshua will need 66 meters of wire to enclose his rectangular garden completely.

    ### Answer: 66 meters

Expected answer: 66

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 18 meters and a width of 11 meters. What is the perimeter of the rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides.

    Given:
    - Length of the rectangle is 18 meters
    - Width of the rectangle is 11 meters

    Step 1: Calculate the perimeter using the formula: Perimeter = 2 × (Length + Width)
    Perimeter = 2 × (18 + 11)
    Perimeter = 2 × 29
    Perimeter = 58 meters

    Therefore, the perimeter of the rectangle is 58 meters.

    ### Answer: 58 meters

Expected answer: 58

Correct? Yes

🔗 Follow-up

Problem: Suppose the width of the rectangle changed to 44 meters, while the length remained at 18 meters. What would be the new perimeter of the rectangle?

Gemma 2B:

    Great! Let's solve this problem using the same method as before.

    Given:
    - Length of the rectangle is 18 meters (unchanged)
    - New width of the rectangle is 44 meters

    Step 1: Calculate the new perimeter using the formula: Perimeter = 2 × (Length + Width)
    Perimeter = 2 × (18 + 44)
    Perimeter = 2 × 62
    Perimeter = 124 meters

    Therefore, with the new width of 44 meters and the length remaining at 18 meters, the new perimeter of the rectangle would be 124 meters.

    ### Answer: 124 meters

Expected answer: 124

Correct? Yes

🔗 Problem

Problem: The dimensions of a rectangle are 22 feet by 39 feet. What is the perimeter of the rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides. Let's solve this step by step:

    1. The rectangle has two sides that are 22 feet long and two sides that are 39 feet long.

    2. The perimeter is the sum of all four sides:
       * Perimeter = 2 × (length + width)
       * Perimeter = 2 × (22 feet + 39 feet)
       * Perimeter = 2 × 61 feet
       * Perimeter = 122 feet

    Therefore, the perimeter of the rectangle is 122 feet.

    ### Answer: 122 feet.

Expected answer: 122

Correct? Yes

🔗 Follow-up

Problem: If the length of the rectangle is now 26 feet instead of 39 feet, while the width remains the same at 22 feet, what would then be the new perimeter of the rectangle?

Gemma 2B:

    Great! Let's solve this problem step by step. We now have a rectangle with a length of 26 feet and a width of 22 feet.

    Given:
    - Length = 26 feet
    - Width = 22 feet

    Step 1: Calculate the perimeter using the formula: Perimeter = 2 × (length + width)

    Perimeter = 2 × (26 feet + 22 feet)
    Perimeter = 2 × 48 feet
    Perimeter = 96 feet

    Therefore, the new perimeter of the rectangle with a length of 26 feet and a width of 22 feet is 96 feet.

    ### Answer: 96 feet.

Expected answer: 96

Correct? Yes

🔗 Problem

Problem: A rectangle has two sides measuring 45m and the other two sides measuring 25m each. What is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add the lengths of all four sides.

    Given:
    - Two sides of the rectangle measure 45m each.
    - The other two sides of the rectangle measure 25m each.

    Step 1: Calculate the total length of the two sides measuring 45m.
    Total length of 45m sides = 2 × 45m = 90m

    Step 2: Calculate the total length of the two sides measuring 25m.
    Total length of 25m sides = 2 × 25m = 50m

    Step 3: Calculate the perimeter by adding the lengths of all four sides.
    Perimeter = Total length of 45m sides + Total length of 25m sides
    Perimeter = 90m + 50m = 140m

    ### Answer: 140m

Expected answer: 140

Correct? Yes

🔗 Follow-up

Problem: In the previous rectangle question, suppose one of the sides measuring 45m was incorrectly assessed. The actual measurement is found to be 42m. With this new information, what would be the adjusted perimeter of the rectangle?

Gemma 2B:

    Let's solve this problem using the new information provided.

    Given:
    - One side of the rectangle that was previously measured as 45m is now found to be 42m.
    - The other side measuring 45m remains unchanged.
    - The other two sides of the rectangle measure 25m each.

    Step 1: Calculate the total length of the two sides measuring 42m and 45m.
    Total length of the updated sides = 42m + 45m = 87m

    Step 2: Calculate the total length of the two sides measuring 25m.
    Total length of 25m sides = 2 × 25m = 50m

    Step 3: Calculate the adjusted perimeter by adding the lengths of all four sides.
    Adjusted perimeter = Total length of the updated sides + Total length of 25m sides
    Adjusted perimeter = 87m + 50m = 137m

    ### Answer: 137m

Expected answer: 134

Correct? No

🔗 Problem

Problem: A rectangular garden has a length of 8m and a width of 5m. What is the perimeter of this garden?

Gemma 2B:

    To find the perimeter of the rectangular garden, we need to add up the lengths of all four sides.

    Given:
    - The length of the garden is 8m.
    - The width of the garden is 5m.

    Step 1: Calculate the perimeter of the garden.
    Perimeter = 2 × (length + width)
    Perimeter = 2 × (8m + 5m)
    Perimeter = 2 × 13m
    Perimeter = 26m

    Therefore, the perimeter of the rectangular garden is 26m.

    ### Answer: 26m

Expected answer: 26

Correct? Yes

🔗 Follow-up

Problem: The owner of the rectangular garden decided to extend its length to 46m while keeping the width the same, i.e., 5m. What is the new perimeter of the garden now?

Gemma 2B:

    Great! Let's solve this problem step by step. We need to find the new perimeter of the garden after the owner extended its length to 46m while keeping the width at 5m.

    Given:
    - The new length of the garden is 46m.
    - The width of the garden remains 5m.

    Step 1: Calculate the new perimeter of the garden.
    Perimeter = 2 × (length + width)
    Perimeter = 2 × (46m + 5m)
    Perimeter = 2 × 51m
    Perimeter = 102m

    Therefore, the new perimeter of the rectangular garden after extending its length is 102m.

    ### Answer: 102m

Expected answer: 102

Correct? Yes

🔗 Problem

Problem: In a rectangle, the length is 19 units and the width is 17 units. What is the area of this rectangle?

Gemma 2B:

    To find the area of a rectangle, we use the formula:

    Area = length × width

    Given:
    - The length of the rectangle is 19 units.
    - The width of the rectangle is 17 units.

    Now, let's calculate the area:

    Area = 19 × 17
    Area = 323

    Therefore, the area of the rectangle is 323 square units.

    ### Answer: 323 square units.

Expected answer: 323

Correct? Yes

🔗 Follow-up

Problem: In the previous rectangle problem, what if the length was 22 units instead of 19 units while the width remained the same at 17 units? What would be the new area of the rectangle?

Gemma 2B:

    Great! Let's solve this problem using the same formula for the area of a rectangle.

    Given:
    - The new length of the rectangle is 22 units.
    - The width of the rectangle remains the same at 17 units.

    Formula:
    Area = length × width

    Now, let's calculate the new area:

    Area = 22 × 17
    Area = 374

    Therefore, with the new length of 22 units and the same width of 17 units, the area of the rectangle is 374 square units.

    ### Answer: 374 square units.

Expected answer: 374

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 42 meters and a width of 8 meters. What is the perimeter of the rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides.

    Given:
    - Length of the rectangle is 42 meters
    - Width of the rectangle is 8 meters

    Step 1: Calculate the perimeter using the formula: Perimeter = 2 × (Length + Width)
    Perimeter = 2 × (42 + 8)
    Perimeter = 2 × 50
    Perimeter = 100 meters

    Therefore, the perimeter of the rectangle is 100 meters.

    ### Answer: 100 meters

Expected answer: 100

Correct? Yes

🔗 Problem

Problem: A rectangle has a width of 16m and a length of 38m. What is the area of this rectangle?

Gemma 2B:

    To find the area of a rectangle, we use the formula:

    Area = length × width

    Given:
    - The width of the rectangle is 16m.
    - The length of the rectangle is 38m.

    Calculation:
    Area = length × width
    Area = 38m × 16m
    Area = <<38*16=608>>608 m²

    Therefore, the area of the rectangle is 608 square meters.

    ### Answer: 608 m²

Expected answer: 608

Correct? Yes

🔗 Follow-up

Problem: In the rectangle from the previous problem, suppose we replace the length of 38m with a new length of 22m. What would the new area of the rectangle be?

Gemma 2B:

    In this problem, we will calculate the new area of the rectangle using the new length of 22m and the same width of 16m.

    Given:
    - The new length of the rectangle is 22m.
    - The width of the rectangle remains 16m.

    Using the formula for the area of a rectangle:
    Area = length × width

    Calculation:
    Area = 22m × 16m
    Area = <<22*16=352>>352 m²

    Therefore, the new area of the rectangle with a length of 22m and a width of 16m is 352 square meters.

    ### Answer: 352 m²

Expected answer: 352

Correct? Yes

🔗 Problem

Problem: Consider a rectangular plot of land. The plot has a length of 28m and a width of 17m. What is the area of the plot?

Gemma 2B:

    To find the area of a rectangular plot, we use the formula:

    Area = length × width

    Given:
    - The length of the plot is 28 meters.
    - The width of the plot is 17 meters.

    Calculation:
    Area = 28 m × 17 m = 476 m²

    Therefore, the area of the rectangular plot is 476 square meters.

    ### Answer: 476 square meters.

Expected answer: 476

Correct? Yes

🔗 Follow-up

Problem: Suppose instead of the original 28m, the length of the rectangular plot of land were only 10m while keeping the width the same at 17m. What would then be the area of the rectangular plot of land?

Gemma 2B:

    Let's solve this problem using the same formula as before:

    Area = length × width

    Given:
    - The new length of the plot is 10 meters.
    - The width of the plot remains the same at 17 meters.

    Calculation:
    Area = 10 m × 17 m = 170 m²

    Therefore, with the new length of 10 meters and the same width of 17 meters, the area of the rectangular plot would be 170 square meters.

    ### Answer: 170 square meters.

Expected answer: 170

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 43m and a width of 41m. What is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides.

    Given:
    - Length of the rectangle is 43m
    - Width of the rectangle is 41m

    The formula for the perimeter of a rectangle is:
    Perimeter = 2 × (length + width)

    Plugging in the values:
    Perimeter = 2 × (43m + 41m)
    Perimeter = 2 × 84m
    Perimeter = 168m

    ### Answer: 168m

Expected answer: 168

Correct? Yes

🔗 Follow-up

Problem: Suppose the rectangle from the previous problem had its length reduced to 18m while keeping the width the same. What would be the new perimeter of the rectangle?

Gemma 2B:

    Let's solve this problem step by step using the information from the previous problem.

    Given:
    - The new length of the rectangle is 18m
    - The width of the rectangle remains the same at 41m

    The formula for the perimeter of a rectangle is:
    Perimeter = 2 × (length + width)

    Plugging in the new values:
    Perimeter = 2 × (18m + 41m)
    Perimeter = 2 × 59m
    Perimeter = 118m

    Therefore, the new perimeter of the rectangle with a length of 18m and a width of 41m is 118m.

    ### Answer: 118m

Expected answer: 118

Correct? Yes

🔗 Problem

Problem: A rectangle has one side that measures 44m, and the other side that measures 17m. What is the perimeter of the rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides. Let's solve this step by step:

    1. The rectangle has two sides that measure 44m each, and two sides that measure 17m each.

    2. To find the total length of the two sides that measure 44m, multiply 44m by 2:
       44m × 2 = 88m

    3. To find the total length of the two sides that measure 17m, multiply 17m by 2:
       17m × 2 = 34m

    4. To find the perimeter, add the total lengths of all four sides:
       88m + 34m = 122m

    Therefore, the perimeter of the rectangle is 122m.

    ### Answer: 122m

Expected answer: 122

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, we considered a rectangle with one side that measures 44m, and the other side that measures 17m. What would be the perimeter of the rectangle if instead the length of the second side were 21m?

Gemma 2B:

    Great! Let's solve this problem using the same steps as before, but with the new length of the second side.

    Given:
    - One side of the rectangle measures 44m.
    - The other side of the rectangle now measures 21m.

    Step 1: Calculate the total length of the two sides that measure 44m.
    Total length of 44m sides = 44m × 2 = 88m

    Step 2: Calculate the total length of the two sides that measure 21m.
    Total length of 21m sides = 21m × 2 = 42m

    Step 3: Calculate the perimeter by adding the total lengths of all four sides.
    Perimeter = Total length of 44m sides + Total length of 21m sides
    Perimeter = 88m + 42m = 130m

    Therefore, if the length of the second side were 21m, the perimeter of the rectangle would be 130m.

    ### Answer: 130m

Expected answer: 130

Correct? Yes

🔗 Problem

Problem: A rectangle's perimeter is twice the sum of its width and length. If the rectangle's width is 2m and its length is 20m, what is its perimeter?

Gemma 2B:

    Let's solve this step by step:

    1. We know that the perimeter of a rectangle is given by the formula:
       Perimeter = 2 × (length + width)

    2. We are given that the width is 2m and the length is 20m. Let's substitute these values into the formula:
       Perimeter = 2 × (20m + 2m)
                 = 2 × 22m
                 = 44m

    Therefore, the perimeter of the rectangle is 44m.

    ### Answer: 44m

Expected answer: 44

Correct? Yes

🔗 Follow-up

Problem: If the width of the rectangle is increased from 2m to 32m, while keeping the length the same at 20m, what is the new perimeter of the rectangle?

Gemma 2B:

    Great! Let's solve this problem step by step using the same formula for the perimeter of a rectangle.

    Given:
    - The new width of the rectangle is 32m.
    - The length of the rectangle remains the same at 20m.

    Step 1: Use the formula for the perimeter of a rectangle.
    Perimeter = 2 × (length + width)

    Step 2: Substitute the new width and the unchanged length into the formula.
    Perimeter = 2 × (20m + 32m)

    Step 3: Simplify the expression inside the parentheses.
    Perimeter = 2 × 52m

    Step 4: Multiply the result by 2.
    Perimeter = 104m

    Therefore, the new perimeter of the rectangle after increasing the width from 2m to 32m is 104m.

    ### Answer: 104m

Expected answer: 104

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 4 meters and a width of 5 meters. What is the perimeter of the rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides.

    Given:
    - Length of the rectangle is 4 meters
    - Width of the rectangle is 5 meters

    The perimeter of a rectangle can be calculated using the formula:
    Perimeter = 2 × (length + width)

    Plugging in the values:
    Perimeter = 2 × (4 meters + 5 meters)
    Perimeter = 2 × 9 meters
    Perimeter = 18 meters

    ### Answer: 18 meters

Expected answer: 18

Correct? Yes

🔗 Follow-up

Problem: Consider the same rectangle from before, but now suppose its length is extended to 42 meters while the width remains 5 meters. What would then be the perimeter of the rectangle?

Gemma 2B:

    Let's solve this problem using the given information and the formula for the perimeter of a rectangle.

    Given:
    - The new length of the rectangle is 42 meters
    - The width of the rectangle remains 5 meters

    As before, the perimeter of a rectangle can be calculated using the formula:
    Perimeter = 2 × (length + width)

    Plugging in the new values:
    Perimeter = 2 × (42 meters + 5 meters)
    Perimeter = 2 × 47 meters
    Perimeter = 94 meters

    ### Answer: 94 meters

Expected answer: 94

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 45m and a width of 37m. What is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides.

    Given:
    - Length of the rectangle = 45m
    - Width of the rectangle = 37m

    In a rectangle, opposite sides are equal in length. So, there are two sides with a length of 45m and two sides with a length of 37m.

    Perimeter = 2 × (length + width)
    Perimeter = 2 × (45m + 37m)
    Perimeter = 2 × 82m
    Perimeter = 164m

    Therefore, the perimeter of the rectangle is 164m.

    ### Answer: 164m

Expected answer: 164

Correct? Yes

🔗 Follow-up

Problem: If the length of the rectangle remains the same at 45m, but the width is increased to 47m, what would be the new perimeter of the rectangle?

Gemma 2B:

    Great! Let's solve this problem step by step. We'll use the same formula for the perimeter of a rectangle, but with the new width.

    Given:
    - Length of the rectangle = 45m (unchanged)
    - New width of the rectangle = 47m

    Perimeter = 2 × (length + width)
    Perimeter = 2 × (45m + 47m)
    Perimeter = 2 × 92m
    Perimeter = 184m

    Therefore, the new perimeter of the rectangle with a length of 45m and a width of 47m is 184m.

    ### Answer: 184m

Expected answer: 184

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 27m and a width of 21m. What is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides.

    Given:
    - Length of the rectangle = 27 m
    - Width of the rectangle = 21 m

    Step 1: Calculate the perimeter using the formula: Perimeter = 2 × (Length + Width)
    Perimeter = 2 × (27 m + 21 m)
    Perimeter = 2 × 48 m
    Perimeter = 96 m

    Therefore, the perimeter of the rectangle is 96 meters.

    ### Answer: 96 meters.

Expected answer: 96

Correct? Yes

🔗 Follow-up

Problem: Suppose we extended the length of the rectangle from the previous problem to 45m, while keeping the width at 21m. What would the new perimeter of this rectangle be?

Gemma 2B:

    Let's solve this problem step by step. We will use the information from the previous problem and update the length to find the new perimeter.

    Given:
    - New length of the rectangle = 45 m
    - Width of the rectangle = 21 m (unchanged)

    Step 1: Calculate the new perimeter using the formula: Perimeter = 2 × (Length + Width)
    New Perimeter = 2 × (45 m + 21 m)
    New Perimeter = 2 × 66 m
    New Perimeter = 132 m

    Therefore, the new perimeter of the rectangle with the updated length is 132 meters.

    ### Answer: 132 meters.

Expected answer: 132

Correct? Yes

🔗 Problem

Problem: A rectangular garden has a length of 30m and a width of 20m. What is the perimeter of the garden?

Gemma 2B:

    To find the perimeter of the rectangular garden, we need to add up the lengths of all four sides.

    Given:
    - Length of the garden = 30m
    - Width of the garden = 20m

    Step 1: Calculate the perimeter of the garden.
    Perimeter = 2 × (Length + Width)
    Perimeter = 2 × (30m + 20m)
    Perimeter = 2 × 50m
    Perimeter = 100m

    Therefore, the perimeter of the rectangular garden is 100 meters.

    ### Answer: 100m

Expected answer: 100

Correct? Yes

🔗 Follow-up

Problem: Suppose the width of the rectangular garden is increased to 48m, while the length remains the same at 30m. What would be the new perimeter of the garden?

Gemma 2B:

    Great! Let's solve this problem step by step. We'll use the same formula for the perimeter of a rectangle, but with the new width.

    Given:
    - Length of the garden = 30m (unchanged)
    - New width of the garden = 48m

    Step 1: Calculate the new perimeter of the garden.
    Perimeter = 2 × (Length + Width)
    Perimeter = 2 × (30m + 48m)
    Perimeter = 2 × 78m
    Perimeter = 156m

    Therefore, with the new width of 48m and the unchanged length of 30m, the new perimeter of the rectangular garden would be 156 meters.

    ### Answer: 156m

Expected answer: 156

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 30m and a width of 27m. What is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to use the formula:

    Perimeter = 2 × (length + width)

    Given:
    - Length of the rectangle = 30m
    - Width of the rectangle = 27m

    Step 1: Substitute the given values into the formula.
    Perimeter = 2 × (30m + 27m)

    Step 2: Simplify the expression inside the parentheses.
    Perimeter = 2 × (57m)

    Step 3: Multiply the result by 2.
    Perimeter = 2 × 57m = 114m

    Therefore, the perimeter of the rectangle is 114m.

    ### Answer: 114m

Expected answer: 114

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 23m and a width of 11m. What is the area of this rectangle?

Gemma 2B:

    To find the area of a rectangle, we multiply its length by its width.

    Given:
    - Length of the rectangle = 23m
    - Width of the rectangle = 11m

    Area of the rectangle = Length × Width
    Area of the rectangle = 23m × 11m
    Area of the rectangle = 253m²

    ### Answer: 253m²

Expected answer: 253

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 3m and a width of 9m. What would be the total perimeter of this rectangle?

Gemma 2B:

    To find the total perimeter of the rectangle, we need to add up the lengths of all four sides.

    Given:
    - Length of the rectangle = 3m
    - Width of the rectangle = 9m

    The perimeter of a rectangle can be calculated using the formula:
    Perimeter = 2 × (Length + Width)

    Plugging in the values:
    Perimeter = 2 × (3m + 9m)
    Perimeter = 2 × 12m
    Perimeter = 24m

    Therefore, the total perimeter of the rectangle is 24m.

    ### Answer: 24m

Expected answer: 24

Correct? Yes

🔗 Follow-up

Problem: Continuing from the previous problem, suppose the length of the rectangle is still 3m, but now the width has increased to 13m. What is the new total perimeter of the rectangle?

Gemma 2B:

    Great! Let's solve this problem using the information from the previous question.

    Given:
    - Length of the rectangle = 3m
    - New width of the rectangle = 13m

    We will use the same formula to calculate the perimeter of the rectangle:
    Perimeter = 2 × (Length + Width)

    Plugging in the new values:
    Perimeter = 2 × (3m + 13m)
    Perimeter = 2 × 16m
    Perimeter = 32m

    Therefore, with the new width of 13m, the total perimeter of the rectangle is now 32m.

    ### Answer: 32m

Expected answer: 32

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 31m and a width of 6m. What is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to use the formula:

    Perimeter = 2 × (length + width)

    Given:
    - Length of the rectangle = 31 m
    - Width of the rectangle = 6 m

    Now, let's calculate the perimeter:

    Perimeter = 2 × (31 m + 6 m)
    Perimeter = 2 × 37 m
    Perimeter = 74 m

    Therefore, the perimeter of the rectangle is 74 meters.

    ### Answer: 74 meters.

Expected answer: 74

Correct? Yes

🔗 Follow-up

Problem: Now consider, if instead of a length of 31m, the rectangle had a length of 43m but the width remained the same at 6m. What would be the new perimeter of this rectangle?

Gemma 2B:

    Great! Let's solve this problem using the same formula as before.

    Given:
    - New length of the rectangle = 43 m
    - Width of the rectangle remains the same = 6 m

    Now, let's calculate the new perimeter:

    Perimeter = 2 × (length + width)
    Perimeter = 2 × (43 m + 6 m)
    Perimeter = 2 × 49 m
    Perimeter = 98 m

    Therefore, with the new length of 43 meters and the same width of 6 meters, the perimeter of the rectangle would be 98 meters.

    ### Answer: 98 meters.

Expected answer: 98

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 12m and a width of 33m. What is the area of this rectangle?

Gemma 2B:

    To find the area of a rectangle, we multiply its length by its width.

    Given:
    - Length of the rectangle = 12m
    - Width of the rectangle = 33m

    Area of the rectangle = Length × Width
    Area of the rectangle = 12m × 33m
    Area of the rectangle = 396 m²

    ### Answer: 396 m²

Expected answer: 396

Correct? Yes

🔗 Follow-up

Problem: Now, consider that the length of the rectangle was initially 18m instead of 12m, while the width remains the same at 33m. What would be the area of the rectangle in this scenario?

Gemma 2B:

    Okay, let's solve this problem with the new information.

    Given:
    - Length of the rectangle = 18m (instead of 12m)
    - Width of the rectangle = 33m

    To find the area of the rectangle, we multiply its length by its width.

    Area of the rectangle = Length × Width
    Area of the rectangle = 18m × 33m
    Area of the rectangle = 594 m²

    ### Answer: 594 m²

Expected answer: 594

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 20m and all of its sides are of equal length. What is the perimeter of this rectangle?

Gemma 2B:

    Let's think through this step-by-step:

    1) A rectangle has two pairs of sides. The opposite sides are equal in length.

    2) You mentioned that the length of the rectangle is 20m and all sides are of equal length. This means that the rectangle is actually a square, because in a square, all sides are equal.

    3) In a square, the length and width are the same. So, if the length is 20m, the width is also 20m.

    4) The perimeter of a rectangle (or a square) is the sum of all its sides. It can be calculated using the formula:

       Perimeter = 2 * (length + width)

    5) Substituting the values:

       Perimeter = 2 * (20m + 20m)
                 = 2 * 40m
                 = 80m

    ### Answer: 80m

Expected answer: 80

Correct? Yes

🔗 Problem

Problem: A rectangular playground has a length of 35m and a width of 9m. What is the perimeter of the playground?

Gemma 2B:

    To find the perimeter of the rectangular playground, we need to add up the lengths of all four sides.

    Given:
    - Length of the playground = 35m
    - Width of the playground = 9m

    In a rectangle, opposite sides are equal in length. So, there are two sides with a length of 35m and two sides with a length of 9m.

    Perimeter = 2 × (length + width)
    Perimeter = 2 × (35m + 9m)
    Perimeter = 2 × 44m
    Perimeter = 88m

    ### Answer: 88m

Expected answer: 88

Correct? Yes

🔗 Follow-up

Problem: Suppose the length of the rectangular playground was initially stated incorrectly and it's actually 26m, while the width remains 9m. What would be the correct perimeter of the playground in this case?

Gemma 2B:

    Thank you for the correction. Let's solve the problem with the updated length.

    Given:
    - Length of the playground = 26m
    - Width of the playground = 9m

    As before, in a rectangle, opposite sides are equal in length. So, there are two sides with a length of 26m and two sides with a length of 9m.

    Perimeter = 2 × (length + width)
    Perimeter = 2 × (26m + 9m)
    Perimeter = 2 × 35m
    Perimeter = 70m

    ### Answer: 70m

Expected answer: 70

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 9m and a width of 25m. What is the area of the rectangle?

Gemma 2B:

    To find the area of a rectangle, we use the formula:

    Area = length × width

    Given:
    - Length of the rectangle = 9 m
    - Width of the rectangle = 25 m

    Calculation:
    Area = 9 m × 25 m
    Area = 225 m²

    Therefore, the area of the rectangle is 225 square meters.

    ### Answer: 225 m²

Expected answer: 225

Correct? Yes

🔗 Follow-up

Problem: Suppose the length of the rectangle was actually 16m and the width remained the same at 9m. What would be the new area of the rectangle in this case?

Gemma 2B:

    In this case, we have:
    - Length of the rectangle = 16 m
    - Width of the rectangle = 9 m

    Using the same formula as before:

    Area = length × width

    Calculation:
    Area = 16 m × 9 m
    Area = 144 m²

    Therefore, if the length of the rectangle is 16 m and the width is 9 m, the area of the rectangle would be 144 square meters.

    ### Answer: 144 m²

Expected answer: 144

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 13m and a width of 43m. What is the area of the rectangle?

Gemma 2B:

    To find the area of a rectangle, we multiply its length by its width.

    Given:
    - Length of the rectangle = 13 m
    - Width of the rectangle = 43 m

    Area of the rectangle = Length × Width
    Area of the rectangle = 13 m × 43 m
    Area of the rectangle = <<13*43=559>>559 m²

    ### Answer: 559 m²

Expected answer: 559

Correct? Yes

🔗 Follow-up

Problem: Suppose we realized later that the width of the rectangle was actually 42m, not 43m. What would then be the area of the rectangle?

Gemma 2B:

    No problem, let's recalculate the area with the corrected width.

    Given:
    - Length of the rectangle = 13 m
    - Width of the rectangle = 42 m (corrected)

    Area of the rectangle = Length × Width
    Area of the rectangle = 13 m × 42 m
    Area of the rectangle = <<13*42=546>>546 m²

    ### Answer: 546 m²

Expected answer: 546

Correct? Yes

🔗 Problem

Problem: A rectangle has a width of 27m and a length of 47m. What is the perimeter of the rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to use the formula:

    Perimeter = 2 × (length + width)

    Given:
    - The width of the rectangle is 27m.
    - The length of the rectangle is 47m.

    Step 1: Substitute the given values into the formula.
    Perimeter = 2 × (47m + 27m)

    Step 2: Simplify the expression inside the parentheses.
    Perimeter = 2 × (74m)

    Step 3: Multiply the result by 2.
    Perimeter = 2 × 74m = 148m

    Therefore, the perimeter of the rectangle is 148m.

    ### Answer: 148m

Expected answer: 148

Correct? Yes

🔗 Follow-up

Problem: Suppose the width of the rectangle is actually 9m instead of 27m. What would be the new perimeter of the rectangle?

Gemma 2B:

    Let's solve this problem using the same steps as before, but with the updated width of 9m.

    Given:
    - The width of the rectangle is now 9m.
    - The length of the rectangle remains 47m.

    Step 1: Substitute the given values into the formula.
    Perimeter = 2 × (length + width)
    Perimeter = 2 × (47m + 9m)

    Step 2: Simplify the expression inside the parentheses.
    Perimeter = 2 × (56m)

    Step 3: Multiply the result by 2.
    Perimeter = 2 × 56m = 112m

    Therefore, with the updated width of 9m, the new perimeter of the rectangle is 112m.

    ### Answer: 112m

Expected answer: 112

Correct? Yes

🔗 Problem

Problem: A rectangular football field has an area of 21m * 42m, calculate the area of the football field.

Gemma 2B:

    To find the area of a rectangle, we multiply its length by its width.

    Given:
    - The length of the football field is 42 meters.
    - The width of the football field is 21 meters.

    Calculation:
    Area = length × width
    Area = 42 m × 21 m
    Area = 882 m²

    Therefore, the area of the rectangular football field is 882 square meters.

    ### Answer: 882 square meters.

Expected answer: 882

Correct? Yes

🔗 Problem

Problem: A rectangle's area is found by multiplying its length by its width. If the width of a certain rectangle is 27m and the length is 25m, what is the area of the rectangle?

Gemma 2B:

    To find the area of the rectangle, we need to multiply its length by its width.

    Given:
    - The width of the rectangle is 27 meters.
    - The length of the rectangle is 25 meters.

    Calculation:
    Area = Length × Width
    Area = 25 m × 27 m
    Area = 675 m²

    Therefore, the area of the rectangle is 675 square meters.

    ### Answer: 675 square meters.

Expected answer: 675

Correct? Yes

🔗 Follow-up

Problem: Suppose the width of the rectangle in the previous problem was not 27m, but was instead 11m, with the length remaining at 25m. What would then be the new area of the rectangle?

Gemma 2B:

    In this new scenario, the width of the rectangle is changed to 11 meters, while the length remains at 25 meters.

    Given:
    - The new width of the rectangle is 11 meters.
    - The length of the rectangle is still 25 meters.

    Calculation:
    New Area = Length × New Width
    New Area = 25 m × 11 m
    New Area = 275 m²

    Therefore, with the new width of 11 meters and the length remaining at 25 meters, the area of the rectangle would be 275 square meters.

    ### Answer: 275 square meters.

Expected answer: 275

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 45m and a width of 48m. What is the perimeter of the rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides.

    Given:
    - Length of the rectangle = 45m
    - Width of the rectangle = 48m

    The perimeter of a rectangle can be calculated using the formula:
    Perimeter = 2 × (Length + Width)

    Plugging in the values:
    Perimeter = 2 × (45m + 48m)
    Perimeter = 2 × 93m
    Perimeter = 186m

    Therefore, the perimeter of the rectangle is 186 meters.

    ### Answer: 186m

Expected answer: 186

Correct? Yes

🔗 Follow-up

Problem: In the previous example, consider if the width of the rectangle was actually 34m instead of 48m. Now, what would be the perimeter of that rectangle?

Gemma 2B:

    Let's solve this problem with the updated width value.

    Given:
    - Length of the rectangle = 45m
    - Width of the rectangle = 34m

    We will use the same formula to calculate the perimeter:
    Perimeter = 2 × (Length + Width)

    Plugging in the updated values:
    Perimeter = 2 × (45m + 34m)
    Perimeter = 2 × 79m
    Perimeter = 158m

    Therefore, with the updated width of 34m, the perimeter of the rectangle is 158 meters.

    ### Answer: 158m

Expected answer: 158

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 11 meters and a width of 7 meters. What is the perimeter of the rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides.

    Given:
    - Length of the rectangle is 11 meters
    - Width of the rectangle is 7 meters

    The perimeter of a rectangle can be calculated using the formula:
    Perimeter = 2 × (length + width)

    Plugging in the values:
    Perimeter = 2 × (11 + 7)
    Perimeter = 2 × 18
    Perimeter = <<2*18=36>>36 meters

    Therefore, the perimeter of the rectangle is 36 meters.

    ### Answer: 36 meters

Expected answer: 36

Correct? Yes

🔗 Follow-up

Problem: Suppose the length of the rectangle was instead 10 meters while the width remained 7 meters. What would be the new perimeter of the rectangle?

Gemma 2B:

    Great! Let's solve this problem using the same method as before.

    Given:
    - The new length of the rectangle is 10 meters
    - The width of the rectangle remains 7 meters

    We will use the same formula to calculate the perimeter:
    Perimeter = 2 × (length + width)

    Plugging in the new values:
    Perimeter = 2 × (10 + 7)
    Perimeter = 2 × 17
    Perimeter = <<2*17=34>>34 meters

    Therefore, with a length of 10 meters and a width of 7 meters, the new perimeter of the rectangle would be 34 meters.

    ### Answer: 34 meters

Expected answer: 34

Correct? Yes

🔗 Problem

Problem: A rectangular field has a length of 30m and a width of 2m. Can you calculate the perimeter of the field?

Gemma 2B:

    To find the perimeter of the rectangular field, we need to add up the lengths of all four sides.

    Given:
    - Length of the field = 30 m
    - Width of the field = 2 m

    The perimeter of a rectangle is calculated using the formula: P = 2(l + w), where P is the perimeter, l is the length, and w is the width.

    Perimeter = 2(30 m + 2 m)
    Perimeter = 2(32 m)
    Perimeter = 64 m

    ### Answer: The perimeter of the rectangular field is 64 m.

Expected answer: 64

Correct? Yes

🔗 Follow-up

Problem: As a follow-up to the previous problem, let's say that the length of the rectangular field is reduced to 20m instead of 30m, while the width remains the same. What would the new perimeter of the field be?

Gemma 2B:

    Great! Let's solve this problem using the same method as before.

    Given:
    - New length of the field = 20 m
    - Width of the field = 2 m (unchanged)

    The perimeter of a rectangle is calculated using the formula: P = 2(l + w), where P is the perimeter, l is the length, and w is the width.

    Perimeter = 2(20 m + 2 m)
    Perimeter = 2(22 m)
    Perimeter = 44 m

    ### Answer: The new perimeter of the rectangular field is 44 m.

Expected answer: 44

Correct? Yes

🔗 Problem

Problem: A rectangle has one side that is 7m long and another side that is 8m long. What is the perimeter of the rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides. Let's solve this step by step:

    1. The rectangle has two sides that are 7m long and two sides that are 8m long.

    2. To find the perimeter, we add the lengths of all four sides:
       * Perimeter = 2 × (length + width)
       * Perimeter = 2 × (7m + 8m)
       * Perimeter = 2 × 15m
       * Perimeter = 30m

    Therefore, the perimeter of the rectangle is 30m.

    ### Answer: 30m

Expected answer: 30

Correct? Yes

🔗 Follow-up

Problem: Consider that the length of the rectangle was originally 19m instead of 7m. How would the new perimeter be calculated then?

Gemma 2B:

    Great! Let's solve this problem with the new length of 19m.

    Given:
    - The rectangle has one side that is 19m long and another side that is 8m long.

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides. Here's how we calculate the new perimeter:

    1. The rectangle has two sides that are 19m long and two sides that are 8m long.

    2. To find the perimeter, we add the lengths of all four sides:
       * Perimeter = 2 × (length + width)
       * Perimeter = 2 × (19m + 8m)
       * Perimeter = 2 × 27m
       * Perimeter = 54m

    Therefore, with the new length of 19m, the perimeter of the rectangle is 54m.

    ### Answer: 54m

Expected answer: 54

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 14m and a width of 18m. What is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides.

    Given:
    - Length of the rectangle is 14m
    - Width of the rectangle is 18m

    Step 1: Calculate the perimeter using the formula: Perimeter = 2 × (Length + Width)
    Perimeter = 2 × (14m + 18m)
    Perimeter = 2 × 32m
    Perimeter = 64m

    Therefore, the perimeter of the rectangle is 64m.

    ### Answer: 64m

Expected answer: 64

Correct? Yes

🔗 Follow-up

Problem: Now let's consider another rectangle. The length of this rectangle is 9m rather than 14m, while the width remains the same at 18m. What is the perimeter of this new rectangle?

Gemma 2B:

    Great! Let's solve this problem using the same method as before.

    Given:
    - Length of the new rectangle is 9m
    - Width of the new rectangle is 18m

    Step 1: Calculate the perimeter using the formula: Perimeter = 2 × (Length + Width)
    Perimeter = 2 × (9m + 18m)
    Perimeter = 2 × 27m
    Perimeter = 54m

    Therefore, the perimeter of the new rectangle with a length of 9m and a width of 18m is 54m.

    ### Answer: 54m

Expected answer: 54

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 43 units and a width of 3 units. Calculate the perimeter of this rectangle.

Gemma 2B:

    To find the perimeter of a rectangle, we use the formula:

    Perimeter = 2 × (length + width)

    Given:
    - Length = 43 units
    - Width = 3 units

    Calculation:
    Perimeter = 2 × (43 + 3)
    Perimeter = 2 × 46
    Perimeter = <<2*46=92>>92 units

    ### Answer: 92 units.

Expected answer: 92

Correct? Yes

🔗 Follow-up

Problem: Let's consider the same rectangle from before, but this time, the width has increased to 39 units while the length remained the same at 43 units. What is the new perimeter of this rectangle?

Gemma 2B:

    Okay, let's solve this problem using the same formula as before:

    Perimeter = 2 × (length + width)

    Given:
    - Length = 43 units (unchanged)
    - Width = 39 units (increased from 3 units)

    Calculation:
    Perimeter = 2 × (43 + 39)
    Perimeter = 2 × 82
    Perimeter = <<2*82=164>>164 units

    ### Answer: 164 units.

Expected answer: 164

Correct? Yes

🔗 Problem

Problem: A rectangle has one side that measures 36 meters and another side that measures 42 meters. What is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides. Let's solve this step by step:

    1. The rectangle has two sides that measure 36 meters each and two sides that measure 42 meters each.

    2. To find the perimeter, we add the lengths of all four sides:
       * Perimeter = 2 × (length + width)
       * Perimeter = 2 × (36 meters + 42 meters)
       * Perimeter = 2 × 78 meters
       * Perimeter = 156 meters

    Therefore, the perimeter of the rectangle is 156 meters.

    ### Answer: 156 meters

Expected answer: 156

Correct? Yes

🔗 Follow-up

Problem: Now suppose that the longer side of the rectangle measures 48 meters instead of 42. What would be the new perimeter of the rectangle?

Gemma 2B:

    Great! Let's solve this problem using the same method as before.

    Given:
    - One side of the rectangle measures 36 meters (unchanged).
    - The longer side of the rectangle now measures 48 meters (instead of 42 meters).

    Step 1: Calculate the perimeter using the formula:
    Perimeter = 2 × (length + width)
    Perimeter = 2 × (36 meters + 48 meters)
    Perimeter = 2 × 84 meters
    Perimeter = 168 meters

    Therefore, with the longer side measuring 48 meters, the new perimeter of the rectangle would be 168 meters.

    ### Answer: 168 meters

Expected answer: 168

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 1m and a width of 6m. What is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to use the formula:

    Perimeter = 2 × (length + width)

    Given:
    - Length of the rectangle = 1 m
    - Width of the rectangle = 6 m

    Now, let's calculate the perimeter:

    Perimeter = 2 × (1 m + 6 m)
    Perimeter = 2 × 7 m
    Perimeter = 14 m

    Therefore, the perimeter of the rectangle is 14 meters.

    ### Answer: 14 meters

Expected answer: 14

Correct? Yes

🔗 Follow-up

Problem: Now consider that the length of the rectangle has changed to 28m, while the width remains at 6m. What is the new perimeter of the rectangle?

Gemma 2B:

    Great! Let's solve this problem using the same formula as before.

    Given:
    - New length of the rectangle = 28 m
    - Width of the rectangle = 6 m (unchanged)

    Perimeter = 2 × (length + width)

    Now, let's calculate the new perimeter:

    Perimeter = 2 × (28 m + 6 m)
    Perimeter = 2 × 34 m
    Perimeter = 68 m

    Therefore, the new perimeter of the rectangle with a length of 28 m and a width of 6 m is 68 meters.

    ### Answer: 68 meters

Expected answer: 68

Correct? Yes

🔗 Problem

Problem: A rectangle has two sides measuring 45m and two sides measuring 8m. What is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides.

    Given:
    - Two sides of the rectangle measure 45m each.
    - The other two sides of the rectangle measure 8m each.

    Step 1: Calculate the total length of the two sides measuring 45m.
    Total length of 45m sides = 2 × 45m = 90m

    Step 2: Calculate the total length of the two sides measuring 8m.
    Total length of 8m sides = 2 × 8m = 16m

    Step 3: Add the lengths of all four sides to find the perimeter.
    Perimeter = Total length of 45m sides + Total length of 8m sides
    Perimeter = 90m + 16m = 106m

    ### Answer: 106m

Expected answer: 106

Correct? Yes

🔗 Problem

Problem: A rectangular garden has a length of 25 meters and a width of 37 meters. What is the perimeter of the garden?

Gemma 2B:

    To find the perimeter of the rectangular garden, we need to add up the lengths of all four sides.

    Given:
    - Length of the garden = 25 meters
    - Width of the garden = 37 meters

    Step 1: Calculate the perimeter of the garden.
    Perimeter = 2 × (Length + Width)
    Perimeter = 2 × (25 + 37)
    Perimeter = 2 × 62
    Perimeter = 124 meters

    Therefore, the perimeter of the rectangular garden is 124 meters.

    ### Answer: 124 meters

Expected answer: 124

Correct? Yes

🔗 Follow-up

Problem: Suppose we reduce the length of the garden from 25 meters to 16 meters, while the width remains unchanged at 37 meters. What would be the new perimeter of the garden?

Gemma 2B:

    Great! Let's calculate the new perimeter of the garden with the updated length.

    Given:
    - New length of the garden = 16 meters
    - Width of the garden = 37 meters (unchanged)

    Step 1: Calculate the new perimeter of the garden.
    New Perimeter = 2 × (New Length + Width)
    New Perimeter = 2 × (16 + 37)
    New Perimeter = 2 × 53
    New Perimeter = 106 meters

    Therefore, the new perimeter of the garden after reducing the length to 16 meters is 106 meters.

    ### Answer: 106 meters

Expected answer: 106

Correct? Yes

🔗 Problem

Problem: A rectangle has length 36m and width 3m. What is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to use the formula:

    Perimeter = 2 × (length + width)

    Given:
    - Length of the rectangle = 36 m
    - Width of the rectangle = 3 m

    Now, let's calculate the perimeter:

    Perimeter = 2 × (36 m + 3 m)
    Perimeter = 2 × 39 m
    Perimeter = 78 m

    Therefore, the perimeter of the rectangle is 78 meters.

    ### Answer: 78 meters

Expected answer: 78

Correct? Yes

🔗 Follow-up

Problem: Suppose we made a change to the rectangle from the previous problem. Instead of a length of 36m, we shortened it to only 1m. What would be the new perimeter of this rectangle?

Gemma 2B:

    Great! Let's solve this problem step by step. We'll use the same formula for the perimeter of a rectangle, but with the updated length.

    Given:
    - New length of the rectangle = 1 m
    - Width of the rectangle = 3 m

    Formula:
    Perimeter = 2 × (length + width)

    Now, let's calculate the new perimeter:

    Perimeter = 2 × (1 m + 3 m)
    Perimeter = 2 × 4 m
    Perimeter = 8 m

    Therefore, the new perimeter of the rectangle with a length of 1 m and a width of 3 m is 8 meters.

    ### Answer: 8 meters

Expected answer: 8

Correct? Yes

🔗 Problem

Problem: A rectangular garden has a length of 45 meters and a width of 50 meters. Calculate the perimeter of the garden.

Gemma 2B:

    To find the perimeter of the rectangular garden, we need to add up the lengths of all four sides.

    Given:
    - Length of the garden = 45 meters
    - Width of the garden = 50 meters

    Step 1: Calculate the perimeter of the garden.
    Perimeter = 2 × (Length + Width)
    Perimeter = 2 × (45 + 50)
    Perimeter = 2 × 95
    Perimeter = 190 meters

    Therefore, the perimeter of the rectangular garden is 190 meters.

    ### Answer: 190 meters

Expected answer: 190

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 44m and a width of 34m. What is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to use the formula:

    Perimeter = 2 × (length + width)

    Given:
    - Length of the rectangle = 44 m
    - Width of the rectangle = 34 m

    Step 1: Substitute the given values into the formula.
    Perimeter = 2 × (44 m + 34 m)

    Step 2: Simplify the expression inside the parentheses.
    Perimeter = 2 × (78 m)

    Step 3: Multiply the result by 2.
    Perimeter = 2 × 78 m = 156 m

    Therefore, the perimeter of the rectangle is 156 meters.

    ### Answer: 156 meters

Expected answer: 156

Correct? Yes

🔗 Follow-up

Problem: Now suppose the width of the rectangle changes to 36m while the length remains the same at 44m. What would be the new perimeter of the rectangle in this case?

Gemma 2B:

    Great! Let's solve this problem using the same formula as before.

    Given:
    - Length of the rectangle = 44 m (unchanged)
    - New width of the rectangle = 36 m

    Step 1: Substitute the given values into the formula.
    Perimeter = 2 × (length + width)
    Perimeter = 2 × (44 m + 36 m)

    Step 2: Simplify the expression inside the parentheses.
    Perimeter = 2 × (80 m)

    Step 3: Multiply the result by 2.
    Perimeter = 2 × 80 m = 160 m

    Therefore, with the new width of 36 meters and the length remaining at 44 meters, the new perimeter of the rectangle would be 160 meters.

    ### Answer: 160 meters

Expected answer: 160

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 42 m and a width of 29 m. Calculate the perimeter of the rectangle.

Gemma 2B:

    To find the perimeter of a rectangle, we use the formula:

    Perimeter = 2 × (length + width)

    Given:
    - Length of the rectangle = 42 m
    - Width of the rectangle = 29 m

    Calculation:
    Perimeter = 2 × (42 m + 29 m)
    Perimeter = 2 × 71 m
    Perimeter = 142 m

    ### Answer: The perimeter of the rectangle is 142 m.

Expected answer: 142

Correct? Yes

🔗 Follow-up

Problem: Suppose the width of the rectangle was actually 38 m instead of 29 m. What would then be the new perimeter of the rectangle?

Gemma 2B:

    Let's solve this problem using the updated width of the rectangle.

    Given:
    - Length of the rectangle = 42 m
    - Updated width of the rectangle = 38 m

    We will use the same formula for the perimeter of a rectangle:
    Perimeter = 2 × (length + width)

    Calculation:
    Perimeter = 2 × (42 m + 38 m)
    Perimeter = 2 × 80 m
    Perimeter = 160 m

    ### Answer: The new perimeter of the rectangle with the updated width of 38 m is 160 m.

Expected answer: 160

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 44 meters and a width of 35 meters. What is the perimeter of the rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides.

    Given:
    - Length of the rectangle is 44 meters
    - Width of the rectangle is 35 meters

    Step 1: Calculate the perimeter using the formula: Perimeter = 2 × (Length + Width)
    Perimeter = 2 × (44 + 35)
    Perimeter = 2 × 79
    Perimeter = 158 meters

    Therefore, the perimeter of the rectangle is 158 meters.

    ### Answer: 158 meters

Expected answer: 158

Correct? Yes

🔗 Follow-up

Problem: Consider the same rectangle from the previous problem, but now the width has changed to 43 meters while the length remains the same at 44 meters. What is the new perimeter of the rectangle?

Gemma 2B:

    Let's solve this problem using the given information and the formula for the perimeter of a rectangle.

    Given:
    - Length of the rectangle is 44 meters (unchanged)
    - New width of the rectangle is 43 meters

    Step 1: Calculate the new perimeter using the formula: Perimeter = 2 × (Length + Width)
    Perimeter = 2 × (44 + 43)
    Perimeter = 2 × 87
    Perimeter = 174 meters

    Therefore, the new perimeter of the rectangle with a length of 44 meters and a width of 43 meters is 174 meters.

    ### Answer: 174 meters

Expected answer: 174

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 44m and a width of 45m. What is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to use the formula:

    Perimeter of a rectangle = 2 × (length + width)

    Given:
    - Length of the rectangle = 44 m
    - Width of the rectangle = 45 m

    Now, let's calculate the perimeter:

    Perimeter = 2 × (44 m + 45 m)
    Perimeter = 2 × 89 m
    Perimeter = 178 m

    Therefore, the perimeter of the rectangle is 178 meters.

    ### Answer: 178 meters.

Expected answer: 178

Correct? Yes

🔗 Follow-up

Problem: The previous rectangle had its width increased from 45m to 48m while keeping the length the same. What is the new perimeter of the rectangle?

Gemma 2B:

    Great! Let's solve this problem step by step. We'll use the same formula for the perimeter of a rectangle as before.

    Given:
    - The length of the rectangle remains the same at 44 m.
    - The width of the rectangle has been increased from 45 m to 48 m.

    Step 1: Use the formula for the perimeter of a rectangle.
    Perimeter of a rectangle = 2 × (length + width)

    Step 2: Substitute the given values into the formula.
    Perimeter = 2 × (44 m + 48 m)

    Step 3: Simplify the expression inside the parentheses.
    Perimeter = 2 × 92 m

    Step 4: Multiply the result by 2.
    Perimeter = 184 m

    Therefore, the new perimeter of the rectangle after increasing its width from 45 m to 48 m is 184 meters.

    ### Answer: 184 meters.

Expected answer: 184

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 3 meters and a width of 39 meters. What is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides. Let's solve this step by step.

    Given:
    - Length of the rectangle = 3 meters
    - Width of the rectangle = 39 meters

    Step 1: Calculate the perimeter of the rectangle using the formula:
    Perimeter = 2 × (Length + Width)

    Step 2: Substitute the given values into the formula:
    Perimeter = 2 × (3 meters + 39 meters)
    Perimeter = 2 × 42 meters

    Step 3: Simplify the expression:
    Perimeter = 84 meters

    Therefore, the perimeter of the rectangle is 84 meters.

    ### Answer: 84 meters

Expected answer: 84

Correct? Yes

🔗 Follow-up

Problem: Suppose the length of the rectangle was actually 17 meters instead of 3 meters, keeping the width the same. What would be the new perimeter of the rectangle now?

Gemma 2B:

    Alright, let's solve this problem with the updated length.

    Given:
    - New length of the rectangle = 17 meters
    - Width of the rectangle = 39 meters

    Step 1: Calculate the perimeter of the rectangle using the formula:
    Perimeter = 2 × (Length + Width)

    Step 2: Substitute the given values into the formula:
    Perimeter = 2 × (17 meters + 39 meters)
    Perimeter = 2 × 56 meters

    Step 3: Simplify the expression:
    Perimeter = 112 meters

    Therefore, with the updated length of 17 meters and the same width of 39 meters, the new perimeter of the rectangle is 112 meters.

    ### Answer: 112 meters

Expected answer: 112

Correct? Yes

🔗 Problem

Problem: A rectangular garden has sides that measure 32m and 12m. What is the perimeter of this garden?

Gemma 2B:

    To find the perimeter of the rectangular garden, we need to add up the lengths of all four sides.

    Given:
    - The length of the garden is 32 meters.
    - The width of the garden is 12 meters.

    Step 1: Calculate the perimeter using the formula: Perimeter = 2 × (length + width)
    Perimeter = 2 × (32 m + 12 m)
    Perimeter = 2 × 44 m
    Perimeter = 88 m

    Therefore, the perimeter of the rectangular garden is 88 meters.

    ### Answer: 88 meters

Expected answer: 88

Correct? Yes

🔗 Problem

Problem: A rectangular swimming pool has a length of 24 feet and a width of 6 feet. What is the perimeter of the swimming pool?

Gemma 2B:

    To find the perimeter of the rectangular swimming pool, we need to add up the lengths of all four sides.

    Given:
    - Length of the pool = 24 feet
    - Width of the pool = 6 feet

    Step 1: Calculate the perimeter of the pool using the formula: Perimeter = 2 × (Length + Width)

    Perimeter = 2 × (24 feet + 6 feet)
    Perimeter = 2 × 30 feet
    Perimeter = 60 feet

    Therefore, the perimeter of the swimming pool is 60 feet.

    ### Answer: 60 feet

Expected answer: 60

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 27m and a width of 21m. What is the area of this rectangle?

Gemma 2B:

    To find the area of a rectangle, we use the formula:

    Area = length × width

    Given:
    - Length of the rectangle is 27m
    - Width of the rectangle is 21m

    Calculation:
    Area = 27m × 21m
    Area = 567 m²

    ### Answer: 567 m²

Expected answer: 567

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, the rectangle had a length of 27m and a width of 21m. Now, consider that the width of the rectangle is instead 8m. What is the area of this rectangle?

Gemma 2B:

    In this problem, we have a rectangle with a different width than the previous problem. Let's solve it using the same formula.

    Given:
    - Length of the rectangle is 27m
    - Width of the rectangle is 8m

    Formula:
    Area = length × width

    Calculation:
    Area = 27m × 8m
    Area = 216 m²

    ### Answer: 216 m²

Expected answer: 216

Correct? Yes

🔗 Problem

Problem: A rectangle has twice the length of a square. If the square's side is 49m, what is the length of the rectangle?

Gemma 2B:

    Let's solve this step by step:

    1. Understand the given information:
       * The rectangle's length is twice the length of the square's side.
       * The square's side is 49 meters.

    2. Calculate the length of the rectangle:
       * Length of the rectangle = 2 × Length of the square's side
       * Length of the rectangle = 2 × 49 meters
       * Length of the rectangle = 98 meters

    Therefore, the length of the rectangle is 98 meters.

    ### Answer: 98 meters

Expected answer: 98

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, we found the length of the rectangle when the square's side was 49m. Now, consider a square with a side length of 18m. What would be the length of the rectangle if it's still twice the length of the square?

Gemma 2B:

    Great! Let's solve this problem using the same approach as before.

    Given:
    - The rectangle's length is twice the length of the square's side.
    - The square's side is 18 meters.

    Step 1: Calculate the length of the rectangle.
    Length of the rectangle = 2 × Length of the square's side
    Length of the rectangle = 2 × 18 meters
    Length of the rectangle = 36 meters

    Therefore, if the square's side is 18 meters and the rectangle's length is twice that of the square's side, the length of the rectangle would be 36 meters.

    ### Answer: 36 meters

Expected answer: 36

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 50m and a width of 36m. What is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to use the formula:

    Perimeter of a rectangle = 2 × (length + width)

    Given:
    - Length of the rectangle = 50m
    - Width of the rectangle = 36m

    Step 1: Add the length and width of the rectangle.
    length + width = 50m + 36m = 86m

    Step 2: Multiply the sum of the length and width by 2 to get the perimeter.
    Perimeter = 2 × (length + width)
    Perimeter = 2 × 86m = 172m

    ### Answer: 172m

Expected answer: 172

Correct? Yes

🔗 Follow-up

Problem: In our previous rectangle, if we now increase the width from 36m to 44m, while keeping the length the same, what will be the new perimeter of the rectangle?

Gemma 2B:

    Let's solve this problem step by step. We'll use the same formula for the perimeter of a rectangle as before:

    Perimeter of a rectangle = 2 × (length + width)

    Given:
    - Length of the rectangle = 50m (unchanged)
    - New width of the rectangle = 44m

    Step 1: Add the length and the new width of the rectangle.
    length + new width = 50m + 44m = 94m

    Step 2: Multiply the sum of the length and the new width by 2 to get the new perimeter.
    New perimeter = 2 × (length + new width)
    New perimeter = 2 × 94m = 188m

    ### Answer: 188m

Expected answer: 188

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 8m and a width of 44m. What is the perimeter of the rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides.

    Given:
    - Length of the rectangle is 8m
    - Width of the rectangle is 44m

    The formula for the perimeter of a rectangle is:
    Perimeter = 2 × (length + width)

    Plugging in the values:
    Perimeter = 2 × (8m + 44m)
    Perimeter = 2 × 52m
    Perimeter = 104m

    Therefore, the perimeter of the rectangle is 104 meters.

    ### Answer: 104 meters.

Expected answer: 104

Correct? Yes

🔗 Follow-up

Problem: Consider the same rectangle from the previous problem, but now its length increases to 40m, while the width remains the same at 44m. What is the new perimeter of the rectangle?

Gemma 2B:

    Let's solve this problem step by step using the given information.

    Given:
    - The new length of the rectangle is 40m
    - The width of the rectangle remains the same at 44m

    As we know, the formula for the perimeter of a rectangle is:
    Perimeter = 2 × (length + width)

    Now, let's plug in the new values:
    Perimeter = 2 × (40m + 44m)
    Perimeter = 2 × 84m
    Perimeter = 168m

    Therefore, the new perimeter of the rectangle with a length of 40m and a width of 44m is 168 meters.

    ### Answer: 168 meters.

Expected answer: 168

Correct? Yes

🔗 Problem

Problem: If a rectangle has a length of 47 feet and a width of 21 feet, what is the area of the rectangle?

Gemma 2B:

    To find the area of a rectangle, we multiply its length by its width.

    Given:
    - The length of the rectangle is 47 feet.
    - The width of the rectangle is 21 feet.

    Calculation:
    Area = length × width
    Area = 47 feet × 21 feet
    Area = 987 square feet

    ### Answer: 987 square feet.

Expected answer: 987

Correct? Yes

🔗 Follow-up

Problem: Now, suppose we adjusted the measurements of the previous rectangle. If the length of the rectangle remained the same at 21 feet, but the width of the rectangle was reduced to 15 feet, what would the new area of the rectangle be?

Gemma 2B:

    In this case, the length and width of the rectangle have been adjusted. Let's calculate the new area using the updated measurements.

    Given:
    - The new length of the rectangle is 21 feet.
    - The new width of the rectangle is 15 feet.

    Calculation:
    Area = length × width
    Area = 21 feet × 15 feet
    Area = 315 square feet

    ### Answer: 315 square feet.

Expected answer: 315

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 19m and a breadth of 28m. What is the perimeter of the rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides.

    Given:
    - Length of the rectangle = 19 m
    - Breadth (width) of the rectangle = 28 m

    The formula for the perimeter of a rectangle is:
    Perimeter = 2 × (Length + Breadth)

    Calculation:
    Perimeter = 2 × (19 m + 28 m)
    Perimeter = 2 × 47 m
    Perimeter = 94 m

    ### Answer: 94 m

Expected answer: 94

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, what if the length of the rectangle was 27m instead of 19m while keeping the breadth the same? What would be the new perimeter?

Gemma 2B:

    Great! Let's solve this problem using the same method as before.

    Given:
    - Length of the rectangle = 27 m
    - Breadth (width) of the rectangle = 28 m

    The formula for the perimeter of a rectangle is:
    Perimeter = 2 × (Length + Breadth)

    Calculation:
    Perimeter = 2 × (27 m + 28 m)
    Perimeter = 2 × 55 m
    Perimeter = 110 m

    ### Answer: 110 m

Expected answer: 110

Correct? Yes

🔗 Problem

Problem: One side of a rectangle is four times the length of the other side. If the longer side measures 39 meters, what is the area of the rectangle when the shorter side is 10 meters?

Gemma 2B:

    Let's solve this step by step:

    1) We know that one side of the rectangle is four times the length of the other side. Let's call the shorter side $x$. Then the longer side is $4x$.

    2) We are told that the longer side measures 39 meters. So we can set up an equation:

       $4x = 39$

    3) Solving for $x$:

       $x = 39 / 4 = 9.75$

       So the shorter side is 9.75 meters.

    4) However, the question asks for the area when the shorter side is 10 meters. So let's calculate the area with the shorter side as 10 meters.

    5) The area of a rectangle is calculated by multiplying the length by the width. If the shorter side is 10 meters, then the longer side is $4 * 10 = 40$ meters.

    6) Area = length * width
            = 40 * 10
            = 400 square meters

    ### Answer: 400 square meters.

Expected answer: 390

Correct? No

🔗 Problem

Problem: A rectangle has identical sides, each measuring 19 meters. What is the total perimeter of the rectangle?

Gemma 2B:

    Let's solve this step by step:

    1) A rectangle has four sides. If the sides are identical, it means that the rectangle is actually a square.

    2) In a square, all sides are equal. Let's call the length of each side 's'. We are told that s = 19 meters.

    3) The perimeter of a square (or any rectangle) is the sum of the lengths of all its sides.

    4) Since all sides are equal, we can calculate the perimeter by multiplying the length of one side by 4.

       Perimeter = 4 * s
                 = 4 * 19
                 = 76

    Therefore, the total perimeter of the square is 76 meters.

    ### Answer: 76 meters.

Expected answer: 76

Correct? Yes

🔗 Follow-up

Problem: The rectangle mentioned in the previous problem has been resized. The new rectangle now has a length of 19 meters but a width of 6 meters. What is the new total perimeter of the rectangle?

Gemma 2B:

    Okay, let's solve this problem step by step:

    1) We are now dealing with a rectangle, not a square. The length and width are different.

    2) We are given that the length of the rectangle is 19 meters and the width is 6 meters.

    3) To find the perimeter of a rectangle, we need to add up the lengths of all four sides.

    4) In a rectangle, opposite sides are equal. So, there are two sides with length 19 meters and two sides with length 6 meters.

    5) The perimeter of the rectangle can be calculated as:

       Perimeter = 2 * (length + width)
                 = 2 * (19 + 6)
                 = 2 * 25
                 = 50

    Therefore, the new total perimeter of the rectangle is 50 meters.

    ### Answer: 50 meters.

Expected answer: 50

Correct? Yes

🔗 Problem

Problem: The area of a rectangle is given by the equation length * width. If the length is 9m and the width is 26m, what is the area of the rectangle?

Gemma 2B:

    To find the area of the rectangle, we need to multiply the length by the width.

    Given:
    - Length = 9m
    - Width = 26m

    Area = Length × Width
    Area = 9m × 26m
    Area = 234 m²

    Therefore, the area of the rectangle is 234 square meters.

    ### Answer: 234 square meters.

Expected answer: 234

Correct? Yes

🔗 Follow-up

Problem: The rectangle now has a new dimension with its length increased to 47m while the width is still 9m. What is the new area of the rectangle?

Gemma 2B:

    In this case, the length has been changed to 47m, while the width remains 9m. Let's calculate the new area using the same formula.

    Given:
    - New length = 47m
    - Width = 9m

    New Area = New Length × Width
    New Area = 47m × 9m
    New Area = 423 m²

    Therefore, the new area of the rectangle with the updated length is 423 square meters.

    ### Answer: 423 square meters.

Expected answer: 423

Correct? Yes

🔗 Problem

Problem: A rectangle has one side measuring 19cm and another side measuring 7cm. What is the perimeter of the rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides. Since opposite sides of a rectangle are equal in length, we can use the following formula:

    Perimeter = 2 × (length + width)

    Given:
    - One side (length) measures 19 cm
    - Another side (width) measures 7 cm

    Calculation:
    Perimeter = 2 × (19 cm + 7 cm)
    Perimeter = 2 × 26 cm
    Perimeter = 52 cm

    ### Answer: 52 cm

Expected answer: 52

Correct? Yes

🔗 Follow-up

Problem: Suppose we extended the rectangle's length from the previous question from 19cm to 21cm. In this case, what would be the new perimeter?

Gemma 2B:

    Great! Let's solve this problem step by step. We'll use the same formula for the perimeter of a rectangle as in the previous question.

    Given:
    - The rectangle's length is now 21 cm (increased from 19 cm)
    - The rectangle's width remains 7 cm

    Formula:
    Perimeter = 2 × (length + width)

    Calculation:
    Perimeter = 2 × (21 cm + 7 cm)
    Perimeter = 2 × 28 cm
    Perimeter = 56 cm

    Therefore, by extending the rectangle's length from 19 cm to 21 cm, the new perimeter of the rectangle is 56 cm.

    ### Answer: 56 cm

Expected answer: 56

Correct? Yes

🔗 Problem

Problem: A shutter is in the shape of a rectangle. Its length is 10m and its width is 6m. What is the total area of the shutter?

Gemma 2B:

    To find the total area of the shutter, we need to use the formula for the area of a rectangle:

    Area of a rectangle = length × width

    Given:
    - The length of the shutter is 10m.
    - The width of the shutter is 6m.

    Now, let's calculate the area:

    Area of the shutter = 10m × 6m
                        = 60m²

    Therefore, the total area of the shutter is 60 square meters.

    ### Answer: 60 square meters.

Expected answer: 60

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 24 units and a width of 15 units. What is the perimeter of the rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides.

    Given:
    - Length of the rectangle = 24 units
    - Width of the rectangle = 15 units

    Step 1: Calculate the perimeter of the rectangle.
    Perimeter = 2 × (Length + Width)
    Perimeter = 2 × (24 + 15)
    Perimeter = 2 × 39
    Perimeter = 78 units

    Therefore, the perimeter of the rectangle is 78 units.

    ### Answer: 78 units.

Expected answer: 78

Correct? Yes

🔗 Follow-up

Problem: Now, imagine the rectangle's width was reduced to 10 units, while the length remained 24 units. What would be the new perimeter of the rectangle under these conditions?

Gemma 2B:

    Great! Let's solve this problem using the new dimensions of the rectangle.

    Given:
    - Length of the rectangle = 24 units (unchanged)
    - New width of the rectangle = 10 units

    Step 1: Calculate the new perimeter of the rectangle.
    Perimeter = 2 × (Length + Width)
    Perimeter = 2 × (24 + 10)
    Perimeter = 2 × 34
    Perimeter = 68 units

    Therefore, with the new width of 10 units and the length remaining at 24 units, the perimeter of the rectangle would be 68 units.

    ### Answer: 68 units.

Expected answer: 68

Correct? Yes

🔗 Problem

Problem: If a rectangular plot of land has a length of 32m and a width of 27m, what is the area of the plot in square meters?

Gemma 2B:

    To find the area of a rectangular plot, we use the formula:

    Area = length × width

    Given:
    - Length of the plot = 32 m
    - Width of the plot = 27 m

    Calculation:
    Area = 32 m × 27 m = <<32*27=864>>864 m²

    Therefore, the area of the rectangular plot is 864 square meters.

    ### Answer: 864 square meters

Expected answer: 864

Correct? Yes

🔗 Follow-up

Problem: In the previous scenario, suppose the width of the rectangular plot of land was actually 18m rather than 27m. What would then be the area of the plot in square meters?

Gemma 2B:

    Let's solve this problem using the updated information.

    Given:
    - Length of the plot = 32 m
    - Width of the plot = 18 m (updated)

    We will use the same formula to calculate the area of the rectangular plot:

    Area = length × width

    Calculation:
    Area = 32 m × 18 m = <<32*18=576>>576 m²

    With the updated width of 18 meters, the area of the rectangular plot is 576 square meters.

    ### Answer: 576 square meters

Expected answer: 576

Correct? Yes

🔗 Problem

Problem: A rectangle has one side that measures 15m and another side that measures 10m. What is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides. Let's solve this step by step:

    1. The rectangle has two sides that measure 15m each and two sides that measure 10m each.

    2. The perimeter is the sum of all four sides:
       * Perimeter = 2 × (length + width)
       * Perimeter = 2 × (15m + 10m)
       * Perimeter = 2 × 25m
       * Perimeter = 50m

    Therefore, the perimeter of the rectangle is 50m.

    ### Answer: 50m

Expected answer: 50

Correct? Yes

🔗 Follow-up

Problem: Now consider the rectangle has one side that measures 33m instead of 15m while the other side still measures 10m. What is the new perimeter of this rectangle?

Gemma 2B:

    Great! Let's solve this problem using the same method as before.

    Given:
    - One side of the rectangle measures 33m.
    - The other side of the rectangle measures 10m.

    Step 1: Calculate the perimeter using the formula: Perimeter = 2 × (length + width)
    * Perimeter = 2 × (33m + 10m)
    * Perimeter = 2 × 43m
    * Perimeter = 86m

    Therefore, the new perimeter of the rectangle with sides measuring 33m and 10m is 86m.

    ### Answer: 86m

Expected answer: 86

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 44m and a width of 37m. What is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to use the formula:

    Perimeter = 2 × (length + width)

    Given:
    - Length of the rectangle = 44m
    - Width of the rectangle = 37m

    Step 1: Substitute the given values into the formula.
    Perimeter = 2 × (44m + 37m)

    Step 2: Simplify the expression inside the parentheses.
    Perimeter = 2 × (81m)

    Step 3: Multiply the result by 2.
    Perimeter = 2 × 81m = 162m

    Therefore, the perimeter of the rectangle is 162m.

    ### Answer: 162m

Expected answer: 162

Correct? Yes

🔗 Follow-up

Problem: What would the perimeter of the rectangle be if the length was 25m instead of 44m but the width remained the same at 37m?

Gemma 2B:

    Great! Let's solve this problem using the same formula as before.

    Given:
    - New length of the rectangle = 25m
    - Width of the rectangle = 37m (unchanged)

    Step 1: Use the formula for the perimeter of a rectangle.
    Perimeter = 2 × (length + width)

    Step 2: Substitute the new length and the unchanged width into the formula.
    Perimeter = 2 × (25m + 37m)

    Step 3: Simplify the expression inside the parentheses.
    Perimeter = 2 × (62m)

    Step 4: Multiply the result by 2.
    Perimeter = 2 × 62m = 124m

    Therefore, if the length of the rectangle is changed to 25m and the width remains at 37m, the new perimeter of the rectangle would be 124m.

    ### Answer: 124m

Expected answer: 124

Correct? Yes

🔗 Problem

Problem: A rectangle has length of 14 cm and width 8 cm. What is the perimeter of the rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides.

    Given:
    - Length of the rectangle = 14 cm
    - Width of the rectangle = 8 cm

    Step 1: Calculate the length of the two longer sides.
    Longer sides = 2 × Length = 2 × 14 cm = 28 cm

    Step 2: Calculate the length of the two shorter sides.
    Shorter sides = 2 × Width = 2 × 8 cm = 16 cm

    Step 3: Add the lengths of all four sides to get the perimeter.
    Perimeter = Longer sides + Shorter sides
    Perimeter = 28 cm + 16 cm = 44 cm

    ### Answer: 44 cm

Expected answer: 44

Correct? Yes

🔗 Follow-up

Problem: If the length of the rectangle remains 14 cm, but the width is increased to 18 cm, what would be the new perimeter of the rectangle now?

Gemma 2B:

    Great! Let's solve this problem using the same steps as before.

    Given:
    - New width of the rectangle = 18 cm
    - Length of the rectangle remains the same = 14 cm

    Step 1: Calculate the length of the two longer sides (unchanged).
    Longer sides = 2 × Length = 2 × 14 cm = 28 cm

    Step 2: Calculate the length of the two shorter sides with the new width.
    Shorter sides = 2 × New width = 2 × 18 cm = 36 cm

    Step 3: Add the lengths of all four sides to get the new perimeter.
    New perimeter = Longer sides + Shorter sides
    New perimeter = 28 cm + 36 cm = 64 cm

    ### Answer: 64 cm

Expected answer: 64

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 26m and a width of 28m. What is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to use the formula:

    Perimeter of a rectangle = 2 × (length + width)

    Given:
    - Length of the rectangle = 26 m
    - Width of the rectangle = 28 m

    Step 1: Add the length and width of the rectangle.
    length + width = 26 m + 28 m = 54 m

    Step 2: Multiply the sum of the length and width by 2 to get the perimeter.
    Perimeter = 2 × (length + width)
    Perimeter = 2 × 54 m = 108 m

    ### Answer: The perimeter of the rectangle is 108 m.

Expected answer: 108

Correct? Yes

🔗 Follow-up

Problem: In the previous scenario, if the rectangle was actually a square with all sides measuring 26m, what would the new perimeter be?

Gemma 2B:

    In this new scenario, we have a square with all sides measuring 26 m. To find the perimeter of the square, we can use the formula:

    Perimeter of a square = 4 × side length

    Given:
    - Side length of the square = 26 m

    Step 1: Multiply the side length by 4 to get the perimeter.
    Perimeter = 4 × side length
    Perimeter = 4 × 26 m = 104 m

    ### Answer: The perimeter of the square with all sides measuring 26 m is 104 m.

Expected answer: 104

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 15m and a width of 37m. What is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides.

    Given:
    - Length of the rectangle is 15m
    - Width of the rectangle is 37m

    The perimeter of a rectangle can be calculated using the formula:
    Perimeter = 2 × (length + width)

    Plugging in the values:
    Perimeter = 2 × (15m + 37m)
    Perimeter = 2 × 52m
    Perimeter = 104m

    Therefore, the perimeter of the rectangle is 104 meters.

    ### Answer: 104m

Expected answer: 104

Correct? Yes

🔗 Follow-up

Problem: The width of the rectangle mentioned in the previous problem is now changed to 19m, while the length is still 15m. What is the new perimeter of this rectangle?

Gemma 2B:

    Let's solve this problem step by step using the information provided.

    Given:
    - The length of the rectangle is still 15m
    - The new width of the rectangle is 19m

    To find the perimeter of a rectangle, we use the formula:
    Perimeter = 2 × (length + width)

    Now, let's plug in the values:
    Perimeter = 2 × (15m + 19m)
    Perimeter = 2 × 34m
    Perimeter = 68m

    Therefore, the new perimeter of the rectangle with a length of 15m and a width of 19m is 68 meters.

    ### Answer: 68m

Expected answer: 68

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 42m and a width of 40m. What is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to use the formula:

    Perimeter of a rectangle = 2 × (length + width)

    Given:
    - Length of the rectangle = 42m
    - Width of the rectangle = 40m

    Step 1: Add the length and width of the rectangle.
    length + width = 42m + 40m = 82m

    Step 2: Multiply the sum of the length and width by 2 to get the perimeter.
    Perimeter = 2 × (length + width)
    Perimeter = 2 × 82m = 164m

    ### Answer: 164m

Expected answer: 164

Correct? Yes

🔗 Follow-up

Problem: The rectangle you were previously given now has a length of 42m and the width has been adjusted to 24m. What is the new perimeter of this rectangle?

Gemma 2B:

    Let's solve this problem using the same formula as before:

    Perimeter of a rectangle = 2 × (length + width)

    Given:
    - New length of the rectangle = 42m
    - New width of the rectangle = 24m

    Step 1: Add the new length and width of the rectangle.
    length + width = 42m + 24m = 66m

    Step 2: Multiply the sum of the new length and width by 2 to get the new perimeter.
    Perimeter = 2 × (length + width)
    Perimeter = 2 × 66m = 132m

    ### Answer: 132m

Expected answer: 132

Correct? Yes

🔗 Problem

Problem: A rectangular garden has one side that measures 21 feet and another side that measures 30 feet. What is the perimeter of the garden?

Gemma 2B:

    To find the perimeter of the rectangular garden, we need to add up the lengths of all four sides. Let's solve this step by step.

    Given:
    - One side of the garden measures 21 feet.
    - Another side of the garden measures 30 feet.

    Step 1: Since the garden is a rectangle, the opposite sides have equal lengths. So, there are two sides measuring 21 feet and two sides measuring 30 feet.

    Step 2: Calculate the perimeter by adding the lengths of all four sides.
    Perimeter = 2 × (length + width)
    Perimeter = 2 × (21 feet + 30 feet)
    Perimeter = 2 × 51 feet
    Perimeter = 102 feet

    Therefore, the perimeter of the rectangular garden is 102 feet.

    ### Answer: 102 feet.

Expected answer: 102

Correct? Yes

🔗 Follow-up

Problem: Now, imagine that the side of the garden that initially measured 30 feet was actually only 5 feet long. What would be the new perimeter of the garden?

Gemma 2B:

    Great! Let's solve this problem with the updated information.

    Given:
    - One side of the garden measures 21 feet.
    - The side that initially measured 30 feet is actually only 5 feet long.

    Step 1: Since the garden is a rectangle, the opposite sides have equal lengths. So, there are two sides measuring 21 feet and two sides measuring 5 feet.

    Step 2: Calculate the perimeter by adding the lengths of all four sides.
    Perimeter = 2 × (length + width)
    Perimeter = 2 × (21 feet + 5 feet)
    Perimeter = 2 × 26 feet
    Perimeter = 52 feet

    Therefore, with the updated side length, the new perimeter of the rectangular garden is 52 feet.

    ### Answer: 52 feet.

Expected answer: 52

Correct? Yes

🔗 Problem

Problem: A certain playground is in the shape of a rectangle. The area of the playground is given as the product of 17 and 44. How many square meters is the playground?

Gemma 2B:

    To find the area of the rectangular playground, we need to multiply the length and width.

    Given:
    - The area of the playground is the product of 17 and 44.

    Step 1: Calculate the area of the playground by multiplying 17 and 44.
    Area = 17 × 44
    Area = 748

    The area of the playground is 748 square meters.

    ### Answer: 748 square meters.

Expected answer: 748

Correct? Yes

🔗 Follow-up

Problem: Let's assume that the length of the playground was mistakenly recorded. Instead of 44m, the correct measurement is 37m. Given this information, how many square meters is the playground now?

Gemma 2B:

    Okay, let's solve this problem with the updated information.

    Given:
    - The length of the playground is 37 meters (instead of 44 meters).
    - The width of the playground is 17 meters.

    Step 1: Calculate the area of the playground by multiplying the length and width.
    Area = length × width
    Area = 37 × 17
    Area = 629

    The area of the playground with the corrected length is 629 square meters.

    ### Answer: 629 square meters.

Expected answer: 629

Correct? Yes

🔗 Problem

Problem: Rectangle ABCD has a width of 47m and a length of 50m. What is the perimeter of the rectangle?

Gemma 2B:

    To find the perimeter of a rectangle, we need to add up the lengths of all four sides. Since opposite sides of a rectangle are equal in length, we can use the formula:

    Perimeter = 2 × (length + width)

    Given:
    - Length of rectangle ABCD = 50m
    - Width of rectangle ABCD = 47m

    Perimeter = 2 × (50m + 47m)
    Perimeter = 2 × 97m
    Perimeter = 194m

    ### Answer: 194m

Expected answer: 194

Correct? Yes

🔗 Follow-up

Problem: Now consider that the rectangle ABCD's dimensions have changed slightly. The width is still 47m, but the length has adjusted to 48m. What is the new perimeter of the rectangle?

Gemma 2B:

    Okay, let's solve this problem using the same method as before.

    Given:
    - New length of rectangle ABCD = 48m
    - Width of rectangle ABCD = 47m

    Using the formula for the perimeter of a rectangle:

    Perimeter = 2 × (length + width)

    Perimeter = 2 × (48m + 47m)
    Perimeter = 2 × 95m
    Perimeter = 190m

    ### Answer: 190m

Expected answer: 190

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 11m and a width of 31m. What is the perimeter of the rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides.

    Given:
    - Length of the rectangle is 11m
    - Width of the rectangle is 31m

    The formula for the perimeter of a rectangle is:
    Perimeter = 2 × (length + width)

    Plugging in the values:
    Perimeter = 2 × (11m + 31m)
    Perimeter = 2 × 42m
    Perimeter = 84m

    Therefore, the perimeter of the rectangle is 84m.

    ### Answer: 84m

Expected answer: 84

Correct? Yes

🔗 Follow-up

Problem: Suppose we later find out that the actual length of the rectangle is 36m, not 11m as we originally thought, while the width remains the same at 31m. What would then be the new perimeter of the rectangle?

Gemma 2B:

    Great! Let's solve this problem with the updated information.

    Given:
    - The actual length of the rectangle is 36m (not 11m as originally thought)
    - The width of the rectangle remains the same at 31m

    We will use the same formula for the perimeter of a rectangle:
    Perimeter = 2 × (length + width)

    Plugging in the updated values:
    Perimeter = 2 × (36m + 31m)
    Perimeter = 2 × 67m
    Perimeter = 134m

    Therefore, with the corrected length of 36m and the unchanged width of 31m, the new perimeter of the rectangle is 134m.

    ### Answer: 134m

Expected answer: 134

Correct? Yes

🔗 Problem

Problem: A rectangular garden has a length of 39m and a width of 19m. What is the area of this garden?

Gemma 2B:

    To find the area of a rectangle, we use the formula:

    Area = length × width

    Given:
    - Length of the garden = 39 m
    - Width of the garden = 19 m

    Calculation:
    Area = 39 m × 19 m
    Area = 741 m²

    Therefore, the area of the rectangular garden is 741 square meters.

    ### Answer: 741 square meters

Expected answer: 741

Correct? Yes

🔗 Follow-up

Problem: If the length of the rectangular garden was actually 35m instead of 39m, keeping the width the same, what would be the new area of the garden?

Gemma 2B:

    Let's solve this problem using the updated length of the garden.

    Given:
    - New length of the garden = 35 m
    - Width of the garden = 19 m

    We will use the same formula to calculate the area of a rectangle:

    Area = length × width

    Calculation:
    Area = 35 m × 19 m
    Area = 665 m²

    Therefore, with the updated length of 35 meters and the same width of 19 meters, the new area of the rectangular garden is 665 square meters.

    ### Answer: 665 square meters

Expected answer: 665

Correct? Yes

🔗 Problem

Problem: A carpenter wants to install a wooden floor in a rectangular hallway. The wooden plank has a width of 29 cm and the carpenter has cut it to a length of 11 cm. How many square centimeters of area does one cut wooden plank cover?

Gemma 2B:

    To find the area covered by one cut wooden plank, we need to multiply its length by its width.

    Given:
    - The width of the wooden plank is 29 cm.
    - The carpenter has cut the plank to a length of 11 cm.

    Area of one cut wooden plank = Length × Width
    Area of one cut wooden plank = 11 cm × 29 cm = <<11*29=319>>319 cm²

    ### Answer: 319 square centimeters

Expected answer: 319

Correct? Yes

🔗 Follow-up

Problem: If instead the carpenter decided to cut the same 29 cm wide wooden plank into shorter lengths of 5 cm each, how many square centimeters of area does one of these shorter cut wooden planks cover?

Gemma 2B:

    In this case, the carpenter is cutting the same 29 cm wide wooden plank into shorter lengths of 5 cm each. We need to calculate the area covered by one of these shorter cut wooden planks.

    Given:
    - The width of the wooden plank is 29 cm.
    - The carpenter has cut the plank to a shorter length of 5 cm.

    Area of one shorter cut wooden plank = Length × Width
    Area of one shorter cut wooden plank = 5 cm × 29 cm = <<5*29=145>>145 cm²

    ### Answer: 145 square centimeters

Expected answer: 145

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 25m and a width of 11m. What is the perimeter of the rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides. In a rectangle, opposite sides have equal lengths.

    Given:
    - Length of the rectangle = 25m
    - Width of the rectangle = 11m

    Step 1: Calculate the perimeter of the rectangle.
    Perimeter = 2 × (Length + Width)
    Perimeter = 2 × (25m + 11m)
    Perimeter = 2 × 36m
    Perimeter = 72m

    Therefore, the perimeter of the rectangle is 72m.

    ### Answer: 72m

Expected answer: 72

Correct? Yes

🔗 Follow-up

Problem: Now, suppose the rectangle's width is changed from 11m to 17m. What will be the new perimeter of the rectangle?

Gemma 2B:

    Great! Let's solve this problem using the same method as before.

    Given:
    - Length of the rectangle = 25m
    - New width of the rectangle = 17m

    Step 1: Calculate the new perimeter of the rectangle.
    New Perimeter = 2 × (Length + New Width)
    New Perimeter = 2 × (25m + 17m)
    New Perimeter = 2 × 42m
    New Perimeter = 84m

    Therefore, the new perimeter of the rectangle with the changed width is 84m.

    ### Answer: 84m

Expected answer: 84

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 49m and a breadth of 9m. What is the perimeter of the rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to use the formula:

    Perimeter of a rectangle = 2 × (length + breadth)

    Given:
    - Length of the rectangle = 49m
    - Breadth of the rectangle = 9m

    Now, let's calculate the perimeter:

    Perimeter = 2 × (49m + 9m)
    Perimeter = 2 × 58m
    Perimeter = 116m

    Therefore, the perimeter of the rectangle is 116m.

    ### Answer: 116m

Expected answer: 116

Correct? Yes

🔗 Follow-up

Problem: Suppose that the breadth of the same rectangle was instead 19m, while the length remains the same at 49m. What would be the new perimeter of the rectangle?

Gemma 2B:

    Great! Let's solve this problem using the same formula for the perimeter of a rectangle.

    Given:
    - Length of the rectangle = 49m
    - New breadth of the rectangle = 19m

    Perimeter of a rectangle = 2 × (length + breadth)

    Now, let's calculate the new perimeter:

    Perimeter = 2 × (49m + 19m)
    Perimeter = 2 × 68m
    Perimeter = 136m

    Therefore, with a length of 49m and a breadth of 19m, the new perimeter of the rectangle is 136m.

    ### Answer: 136m

Expected answer: 136

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 16m and a width of 7m. What is the area of this rectangle?

Gemma 2B:

    To find the area of a rectangle, we use the formula:

    Area = length × width

    Given:
    - Length of the rectangle is 16m
    - Width of the rectangle is 7m

    Calculation:
    Area = 16m × 7m = <<16*7=112>>112m²

    ### Answer: 112m²

Expected answer: 112

Correct? Yes

🔗 Problem

Problem: The perimeter of a rectangular playground is found by the formula 2*(Length + Breadth). If the length of the playground is 14m and the breadth is 2m, what is the perimeter of the playground?

Gemma 2B:

    To find the perimeter of the rectangular playground, we can use the given formula and the provided dimensions.

    Given:
    - The formula for the perimeter of a rectangle is 2 * (Length + Breadth)
    - The length of the playground is 14 meters
    - The breadth (width) of the playground is 2 meters

    Step 1: Substitute the given values into the formula.
    Perimeter = 2 * (Length + Breadth)
    Perimeter = 2 * (14 + 2)

    Step 2: Simplify the expression inside the parentheses.
    Perimeter = 2 * (16)

    Step 3: Multiply the result by 2.
    Perimeter = 2 * 16
    Perimeter = <<2*16=32>>32 meters

    Therefore, the perimeter of the rectangular playground is 32 meters.

    ### Answer: 32 meters

Expected answer: 32

Correct? Yes

🔗 Follow-up

Problem: Now, consider that the breadth of the rectangular playground is changed to 3m, keeping the length the same as before (14m). What is the new perimeter of the playground?

Gemma 2B:

    Great! Let's solve this problem using the same formula and steps as before, but with the updated breadth value.

    Given:
    - The formula for the perimeter of a rectangle is 2 * (Length + Breadth)
    - The length of the playground remains 14 meters
    - The new breadth (width) of the playground is 3 meters

    Step 1: Substitute the given values into the formula.
    Perimeter = 2 * (Length + Breadth)
    Perimeter = 2 * (14 + 3)

    Step 2: Simplify the expression inside the parentheses.
    Perimeter = 2 * (17)

    Step 3: Multiply the result by 2.
    Perimeter = 2 * 17
    Perimeter = <<2*17=34>>34 meters

    Therefore, with the updated breadth of 3 meters and the length remaining at 14 meters, the new perimeter of the rectangular playground is 34 meters.

    ### Answer: 34 meters

Expected answer: 34

Correct? Yes

🔗 Problem

Problem: A square has a side length of 16 units. What is the perimeter of the square?

Gemma 2B:

    To find the perimeter of the square, we need to use the following formula:

    Perimeter of a square = 4 × side length

    Given:
    - The side length of the square is 16 units.

    Calculation:
    Perimeter = 4 × 16
    Perimeter = 64 units

    Therefore, the perimeter of the square with a side length of 16 units is 64 units.

    ### Answer: 64 units.

Expected answer: 64

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, the square's side length was 16 units. Now consider a rectangle with a length of 22 units and a width of 16 units. What is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to use the following formula:

    Perimeter of a rectangle = 2 × (length + width)

    Given:
    - The length of the rectangle is 22 units.
    - The width of the rectangle is 16 units.

    Calculation:
    Perimeter = 2 × (22 + 16)
    Perimeter = 2 × 38
    Perimeter = 76 units

    Therefore, the perimeter of the rectangle with a length of 22 units and a width of 16 units is 76 units.

    ### Answer: 76 units.

Expected answer: 76

Correct? Yes

🔗 Problem

Problem: A rectangular garden has a width of 7 meters and a length of 21 meters. What is the perimeter of this garden?

Gemma 2B:

    To find the perimeter of the rectangular garden, we need to add up the lengths of all four sides. Let's solve this step by step:

    1. The garden has a width of 7 meters and a length of 21 meters.
    2. In a rectangle, opposite sides have equal lengths.
    3. So, there are two sides with a length of 7 meters and two sides with a length of 21 meters.
    4. To find the perimeter, we add up the lengths of all four sides:
       * Perimeter = 2 × (length + width)
       * Perimeter = 2 × (21 meters + 7 meters)
       * Perimeter = 2 × 28 meters
       * Perimeter = 56 meters

    Therefore, the perimeter of the rectangular garden is 56 meters.

    ### Answer: 56 meters

Expected answer: 56

Correct? Yes

🔗 Follow-up

Problem: The width of the garden remains the same, but the length is reduced to 17 meters. Now, what is the new perimeter of the garden?

Gemma 2B:

    Great! Let's solve this problem step by step. We'll use the same formula for the perimeter of a rectangle, but with the updated length.

    Given:
    - The width of the garden is still 7 meters.
    - The new length of the garden is 17 meters.

    Step 1: Use the formula for the perimeter of a rectangle.
    Perimeter = 2 × (length + width)

    Step 2: Substitute the given values into the formula.
    Perimeter = 2 × (17 meters + 7 meters)

    Step 3: Simplify the expression inside the parentheses.
    Perimeter = 2 × (24 meters)

    Step 4: Multiply the result by 2.
    Perimeter = 48 meters

    Therefore, with the new length of 17 meters and the same width of 7 meters, the new perimeter of the garden is 48 meters.

    ### Answer: 48 meters

Expected answer: 48

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 20 meters and a width of 5 meters. What is the area of the rectangle?

Gemma 2B:

    To find the area of a rectangle, we use the formula:

    Area = length × width

    Given:
    - Length of the rectangle is 20 meters
    - Width of the rectangle is 5 meters

    Calculation:
    Area = 20 meters × 5 meters
    Area = 100 square meters

    ### Answer: 100 square meters.

Expected answer: 100

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, we calculated the area of a rectangle with a length of 20 meters and a width of 5 meters. This time, instead of having the width as 5 meters, we have a new rectangle where the width is 17 meters. With the length still being 20 meters, what is the area of this new rectangle?

Gemma 2B:

    Great! Let's solve this problem using the same formula as before.

    Given:
    - Length of the new rectangle is 20 meters (same as the previous problem)
    - Width of the new rectangle is 17 meters

    The formula for the area of a rectangle is:
    Area = length × width

    Calculation:
    Area = 20 meters × 17 meters
    Area = 340 square meters

    Therefore, the area of the new rectangle with a length of 20 meters and a width of 17 meters is 340 square meters.

    ### Answer: 340 square meters.

Expected answer: 340

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 37m and a width of 43m. What is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides.

    Given:
    - Length of the rectangle = 37m
    - Width of the rectangle = 43m

    In a rectangle, opposite sides are equal in length. So, there are two sides with a length of 37m and two sides with a length of 43m.

    Perimeter = 2 × (length + width)
    Perimeter = 2 × (37m + 43m)
    Perimeter = 2 × 80m
    Perimeter = 160m

    ### Answer: 160m

Expected answer: 160

Correct? Yes

🔗 Follow-up

Problem: Suppose the length of the rectangle is now changed to 32m while the width remains the same at 43m. What will be the new perimeter of the rectangle?

Gemma 2B:

    Great! Let's solve this problem step by step. We'll use the same formula for the perimeter of a rectangle, but with the updated length.

    Given:
    - New length of the rectangle = 32m
    - Width of the rectangle = 43m (unchanged)

    Perimeter = 2 × (length + width)
    Perimeter = 2 × (32m + 43m)
    Perimeter = 2 × 75m
    Perimeter = 150m

    Therefore, the new perimeter of the rectangle with a length of 32m and a width of 43m is 150m.

    ### Answer: 150m

Expected answer: 150

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 9m. If the width of the rectangle is 1m, what is the area?

Gemma 2B:

    To find the area of a rectangle, we use the formula:

    Area = length × width

    Given:
    - The length of the rectangle is 9m.
    - The width of the rectangle is 1m.

    Let's plug in the values into the formula:

    Area = 9m × 1m
    Area = 9m²

    Therefore, the area of the rectangle is 9 square meters.

    ### Answer: 9m²

Expected answer: 9

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, we considered a rectangle with a length of 9m and a width of 1m. Now, consider if the width of the rectangle was actually 40m instead of 1m. What would be the new area of the rectangle?

Gemma 2B:

    Great! Let's solve this problem using the same formula for the area of a rectangle.

    Given:
    - The length of the rectangle is 9m.
    - The width of the rectangle is now 40m.

    Area = length × width

    Let's plug in the new values into the formula:

    Area = 9m × 40m
    Area = 360m²

    Therefore, with a length of 9m and a width of 40m, the new area of the rectangle is 360 square meters.

    ### Answer: 360m²

Expected answer: 360

Correct? Yes

🔗 Problem

Problem: A rectangle's area is the product of 22m and 23m. What is the area of the rectangle?

Gemma 2B:

    To find the area of the rectangle, we need to multiply the length and width.

    Given:
    - Length of the rectangle is 22m
    - Width of the rectangle is 23m

    The formula for the area of a rectangle is:
    Area = length × width

    Let's calculate the area:
    Area = 22m × 23m
    Area = 506 m²

    Therefore, the area of the rectangle is 506 square meters.

    ### Answer: 506 square meters

Expected answer: 506

Correct? Yes

🔗 Follow-up

Problem: What if we reconsider the area of the rectangle, but this time its width is 6m instead of 23m, while maintaining the length at 22m. What would then be the area of the rectangle?

Gemma 2B:

    Great! Let's solve this problem with the updated information.

    Given:
    - Length of the rectangle is 22m
    - Width of the rectangle is now 6m

    As before, we'll use the formula for the area of a rectangle:
    Area = length × width

    Now, let's calculate the area with the new width:
    Area = 22m × 6m
    Area = 132 m²

    Therefore, with the updated width of 6 meters and the length of 22 meters, the area of the rectangle is 132 square meters.

    ### Answer: 132 square meters

Expected answer: 132

Correct? Yes

🔗 Problem

Problem: A rectangle has one side that measures 14 cm and another side that measures 21 cm. What is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides. Let's solve this step by step:

    1. The rectangle has two sides that measure 14 cm and two sides that measure 21 cm.

    2. To find the perimeter, we add the lengths of all four sides:
       * Perimeter = 2 × (length + width)
       * Perimeter = 2 × (14 cm + 21 cm)
       * Perimeter = 2 × 35 cm
       * Perimeter = 70 cm

    Therefore, the perimeter of the rectangle is 70 cm.

    ### Answer: 70 cm

Expected answer: 70

Correct? Yes

🔗 Follow-up

Problem: Consider the previous rectangle and suppose its side that previously measured 21 cm now measures 47 cm. What is the new perimeter of this rectangle?

Gemma 2B:

    Great! Let's solve this problem step by step. We'll use the information from the previous problem and update the length of one side to find the new perimeter.

    Given:
    - The rectangle has one side that measures 14 cm (unchanged).
    - The side that previously measured 21 cm now measures 47 cm.

    Step 1: Identify the length and width of the rectangle.
    Length = 47 cm
    Width = 14 cm

    Step 2: Calculate the perimeter using the formula: Perimeter = 2 × (length + width)
    Perimeter = 2 × (47 cm + 14 cm)
    Perimeter = 2 × 61 cm
    Perimeter = 122 cm

    Therefore, the new perimeter of the rectangle is 122 cm.

    ### Answer: 122 cm

Expected answer: 122

Correct? Yes

🔗 Problem

Problem: In Clara's backyard, there is a rectangular swimming pool. The length of the pool is 23 meters, while the width is 12 meters. What is the area of the swimming pool in Clara's backyard?

Gemma 2B:

    To find the area of the rectangular swimming pool, we need to multiply its length by its width.

    Given:
    - The length of the pool is 23 meters.
    - The width of the pool is 12 meters.

    Calculation:
    Area = length × width
    Area = 23 meters × 12 meters
    Area = 276 square meters

    Therefore, the area of the swimming pool in Clara's backyard is 276 square meters.

    ### Answer: 276 square meters.

Expected answer: 276

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 39 meters and a width of 8 meters. What is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to use the formula:

    Perimeter of a rectangle = 2 × (length + width)

    Given:
    - Length of the rectangle = 39 meters
    - Width of the rectangle = 8 meters

    Step 1: Add the length and width of the rectangle.
    length + width = 39 + 8 = 47 meters

    Step 2: Multiply the sum of the length and width by 2 to get the perimeter.
    Perimeter = 2 × (length + width)
    Perimeter = 2 × (39 + 8)
    Perimeter = 2 × 47
    Perimeter = 94 meters

    Therefore, the perimeter of the rectangle is 94 meters.

    ### Answer: 94 meters

Expected answer: 94

Correct? Yes

🔗 Follow-up

Problem: Suppose the width of the rectangle was actually 23 meters instead of 8 meters. What would the perimeter of the rectangle be in this case?

Gemma 2B:

    Let's solve this problem using the same method as before, but with the updated width of 23 meters.

    Given:
    - Length of the rectangle = 39 meters
    - Width of the rectangle = 23 meters

    Step 1: Add the length and width of the rectangle.
    length + width = 39 + 23 = 62 meters

    Step 2: Multiply the sum of the length and width by 2 to get the perimeter.
    Perimeter = 2 × (length + width)
    Perimeter = 2 × (39 + 23)
    Perimeter = 2 × 62
    Perimeter = 124 meters

    Therefore, if the width of the rectangle is 23 meters, the perimeter of the rectangle would be 124 meters.

    ### Answer: 124 meters

Expected answer: 124

Correct? Yes

🔗 Problem

Problem: A rectangle has a width of 27m and a length of 40m. What is the perimeter of the rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides.

    Given:
    - The width of the rectangle is 27m.
    - The length of the rectangle is 40m.

    Step 1: Calculate the perimeter of the rectangle.
    Perimeter = 2 × (length + width)
    Perimeter = 2 × (40m + 27m)
    Perimeter = 2 × 67m
    Perimeter = 134m

    Therefore, the perimeter of the rectangle is 134m.

    ### Answer: 134m

Expected answer: 134

Correct? Yes

🔗 Follow-up

Problem: What if the length of the rectangle was 44m instead of 40m while keeping the width still at 27m? What would the new perimeter of the rectangle be?

Gemma 2B:

    Great! Let's solve this problem with the updated length of 44m and the same width of 27m.

    Given:
    - The width of the rectangle is 27m.
    - The length of the rectangle is now 44m.

    Step 1: Calculate the perimeter of the rectangle with the new length.
    Perimeter = 2 × (length + width)
    Perimeter = 2 × (44m + 27m)
    Perimeter = 2 × 71m
    Perimeter = 142m

    Therefore, with the updated length of 44m and the width of 27m, the new perimeter of the rectangle is 142m.

    ### Answer: 142m

Expected answer: 142

Correct? Yes

🔗 Problem

Problem: A rectangle's length is 35m and its width is 9m. What is the perimeter of the rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to use the formula:

    Perimeter = 2 × (length + width)

    Given:
    - Length of the rectangle = 35m
    - Width of the rectangle = 9m

    Step 1: Substitute the given values into the formula.
    Perimeter = 2 × (35m + 9m)

    Step 2: Simplify the expression inside the parentheses.
    Perimeter = 2 × (44m)

    Step 3: Multiply the result by 2.
    Perimeter = 2 × 44m = 88m

    Therefore, the perimeter of the rectangle is 88m.

    ### Answer: 88m

Expected answer: 88

Correct? Yes

🔗 Follow-up

Problem: Suppose we resized the rectangle and shortened its length from 35m to 19m, while keeping the width the same. What would the new perimeter of the rectangle be?

Gemma 2B:

    Great! Let's solve this problem using the same formula as before.

    Given:
    - New length of the rectangle = 19m
    - Width of the rectangle remains the same = 9m

    Step 1: Use the formula for the perimeter of a rectangle.
    Perimeter = 2 × (length + width)

    Step 2: Substitute the new length and the unchanged width into the formula.
    Perimeter = 2 × (19m + 9m)

    Step 3: Simplify the expression inside the parentheses.
    Perimeter = 2 × (28m)

    Step 4: Multiply the result by 2.
    Perimeter = 2 × 28m = 56m

    Therefore, the new perimeter of the rectangle after shortening its length to 19m is 56m.

    ### Answer: 56m

Expected answer: 56

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 38m and a width of 11m. What is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to use the formula:

    Perimeter = 2 × (length + width)

    Given:
    - Length of the rectangle = 38m
    - Width of the rectangle = 11m

    Step 1: Substitute the given values into the formula.
    Perimeter = 2 × (38m + 11m)

    Step 2: Simplify the expression inside the parentheses.
    Perimeter = 2 × (49m)

    Step 3: Multiply the result by 2.
    Perimeter = 2 × 49m = 98m

    Therefore, the perimeter of the rectangle is 98m.

    ### Answer: 98m

Expected answer: 98

Correct? Yes

🔗 Follow-up

Problem: In the rectangle mentioned earlier, suppose we now construct another rectangle such that its length remains the same (38m), but the width is now 23m instead of 11m. How would the perimeter of this new rectangle be calculated?

Gemma 2B:

    Great! Let's solve this problem step by step. We'll use the same formula for the perimeter of a rectangle as before.

    Given:
    - Length of the new rectangle = 38m (same as the previous rectangle)
    - Width of the new rectangle = 23m (instead of 11m)

    Step 1: Use the formula for the perimeter of a rectangle.
    Perimeter = 2 × (length + width)

    Step 2: Substitute the given values into the formula.
    Perimeter = 2 × (38m + 23m)

    Step 3: Simplify the expression inside the parentheses.
    Perimeter = 2 × (61m)

    Step 4: Multiply the result by 2.
    Perimeter = 2 × 61m = 122m

    Therefore, the perimeter of the new rectangle with a length of 38m and a width of 23m is 122m.

    ### Answer: 122m

Expected answer: 122

Correct? Yes

🔗 Problem

Problem: One side of a rectangle is 28m long, and the other side is 29m long. What is the area of this rectangle?

Gemma 2B:

    To find the area of a rectangle, we multiply the length by the width.

    Given:
    - One side of the rectangle is 28m long.
    - The other side of the rectangle is 29m long.

    Step 1: Identify the length and width of the rectangle.
    Length = 29m
    Width = 28m

    Step 2: Calculate the area by multiplying the length by the width.
    Area = Length × Width
    Area = 29m × 28m
    Area = 812m²

    Therefore, the area of the rectangle is 812 square meters.

    ### Answer: 812m²

Expected answer: 812

Correct? Yes

🔗 Follow-up

Problem: Suppose the side of the rectangle previously mentioned gets extended to 35m instead of 29m, while the other side remains 28m. What would be the new area of the rectangle in this case?

Gemma 2B:

    Great! Let's solve this problem step by step. We'll use the same formula for the area of a rectangle, but with the updated length.

    Given:
    - One side of the rectangle remains 28m long.
    - The other side of the rectangle is now extended to 35m long.

    Step 1: Identify the length and width of the rectangle.
    Length = 35m
    Width = 28m

    Step 2: Calculate the area by multiplying the length by the width.
    Area = Length × Width
    Area = 35m × 28m
    Area = 980m²

    Therefore, the new area of the rectangle with the extended side is 980 square meters.

    ### Answer: 980m²

Expected answer: 980

Correct? Yes

🔗 Problem

Problem: A square has a side length of 9m. What is the total length of fencing needed to enclose the square's perimeter?

Gemma 2B:

    To solve this problem, let's follow these steps:

    1. Understand the given information:
       * The shape is a square.
       * The side length of the square is 9 meters.

    2. Recall the formula for the perimeter of a square:
       * Perimeter of a square = 4 × side length

    3. Calculate the perimeter by plugging in the side length:
       * Perimeter = 4 × 9 meters
       * Perimeter = 36 meters

    Therefore, the total length of fencing needed to enclose the square's perimeter is 36 meters.

    ### Answer: 36 meters

Expected answer: 36

Correct? Yes

🔗 Problem

Problem: A rectangle has a length of 38m and a width of 29m. What is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides.

    Given:
    - Length of the rectangle is 38m
    - Width of the rectangle is 29m

    The perimeter of a rectangle can be calculated using the formula:
    Perimeter = 2 × (length + width)

    Plugging in the values:
    Perimeter = 2 × (38m + 29m)
    Perimeter = 2 × 67m
    Perimeter = 134m

    Therefore, the perimeter of the rectangle is 134 meters.

    ### Answer: 134m

Expected answer: 134

Correct? Yes

🔗 Follow-up

Problem: Now consider that the rectangle from the previous question actually had a length of 6m instead of 38m. What would be the new perimeter of the rectangle?

Gemma 2B:

    Let's update the given information and recalculate the perimeter:

    Given:
    - Length of the rectangle is 6m (updated)
    - Width of the rectangle is 29m

    Using the same formula as before:
    Perimeter = 2 × (length + width)

    Plugging in the updated values:
    Perimeter = 2 × (6m + 29m)
    Perimeter = 2 × 35m
    Perimeter = 70m

    Therefore, with the updated length of 6m, the new perimeter of the rectangle is 70 meters.

    ### Answer: 70m

Expected answer: 70

Correct? Yes

🔗 Problem

Problem: A rectangle has one side of length 45m and another side of length 47m. Find the perimeter of the rectangle.

Gemma 2B:

    To find the perimeter of the rectangle, we need to add up the lengths of all four sides. Since opposite sides of a rectangle are equal in length, we can use the following formula:

    Perimeter = 2 × (length + width)

    Given:
    - One side (length) of the rectangle is 45m.
    - Another side (width) of the rectangle is 47m.

    Calculation:
    Perimeter = 2 × (45m + 47m)
    Perimeter = 2 × 92m
    Perimeter = 184m

    ### Answer: The perimeter of the rectangle is 184m.

Expected answer: 184

Correct? Yes

🔗 Follow-up

Problem: Suppose the length of one side of the rectangle is altered from 47m to 46m. What would be the new perimeter of the rectangle now?

Gemma 2B:

    Great! Let's solve this problem step by step. We'll use the same formula for the perimeter of a rectangle, but with the updated length.

    Given:
    - One side (length) of the rectangle remains 45m.
    - The other side (width) of the rectangle is changed from 47m to 46m.

    Calculation:
    Perimeter = 2 × (length + width)
    Perimeter = 2 × (45m + 46m)
    Perimeter = 2 × 91m
    Perimeter = 182m

    ### Answer: The new perimeter of the rectangle is 182m.

Expected answer: 182

Correct? Yes

🔗 Problem

Problem: Given a rectangle where the length is 24m and the width is 20m, what is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of a rectangle, we use the formula:

    Perimeter = 2 × (length + width)

    Given:
    - Length of the rectangle is 24m
    - Width of the rectangle is 20m

    Calculation:
    Perimeter = 2 × (24m + 20m)
    Perimeter = 2 × 44m
    Perimeter = 88m

    ### Answer: The perimeter of the rectangle is 88m.

Expected answer: 88

Correct? Yes

🔗 Follow-up

Problem: Continuing from the previous scenario, imagine the length of the rectangle stayed the same at 24m, but the width was reduced to 17m. Now, what would be the new perimeter of this rectangle?

Gemma 2B:

    Great! Let's solve this problem using the same formula as before.

    Given:
    - Length of the rectangle is still 24m
    - New width of the rectangle is 17m

    Formula:
    Perimeter = 2 × (length + width)

    Calculation:
    Perimeter = 2 × (24m + 17m)
    Perimeter = 2 × 41m
    Perimeter = 82m

    ### Answer: The new perimeter of the rectangle with a length of 24m and a width of 17m is 82m.

Expected answer: 82

Correct? Yes

🔗 Problem

Problem: The length and width of a rectangle are both 32m. What is the perimeter of this rectangle?

Gemma 2B:

    To find the perimeter of the rectangle, we need to use the formula:

    Perimeter of a rectangle = 2 × (length + width)

    Given:
    - The length of the rectangle is 32m.
    - The width of the rectangle is also 32m.

    Now, let's calculate the perimeter:

    Perimeter = 2 × (32m + 32m)
    Perimeter = 2 × 64m
    Perimeter = 128m

    Therefore, the perimeter of the rectangle is 128m.

    ### Answer: 128m

Expected answer: 128

Correct? Yes

🔗 Follow-up

Problem: The length of the rectangle from the previous problem remains the same, but the width of the rectangle is now adjusted to 13m. What is the new perimeter of this rectangle?

Gemma 2B:

    In the previous problem, we had a rectangle with a length of 32m and a width of 32m. Now, the width has been changed to 13m, while the length remains the same.

    To find the new perimeter of the rectangle, we will use the same formula as before:

    Perimeter of a rectangle = 2 × (length + width)

    Given:
    - The length of the rectangle is still 32m.
    - The new width of the rectangle is 13m.

    Let's calculate the new perimeter:

    Perimeter = 2 × (32m + 13m)
    Perimeter = 2 × 45m
    Perimeter = 90m

    Therefore, the new perimeter of the rectangle with a length of 32m and a width of 13m is 90m.

    ### Answer: 90m

Expected answer: 90

Correct? Yes