🔗 Problem

Problem: The perimeter of a rectangular swimming pool is 324 meters. The length of the pool is 83 meters. What is the width of the pool?

Gemma 2B:

      To find the width of the pool, we can use the formula for the perimeter of a rectangle, which is:

    Perimeter = 2(l + w)

    where l is the length and w is the width.

    We are given that the perimeter is 324 meters and the length is 83 meters, so we can substitute these values into the formula to get:

    324 = 2(83 + w)

    Simplifying this equation, we get:

    324 = 166 + 2w

    Subtracting 166 from both sides gives us:

    158 = 2w

    Dividing both sides by 2 gives us:

    79 = w

    Therefore, the width of the pool is 79 meters.

Expected answer: 79

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 40m. What is the length of each side?

Gemma 2B:

      To find the length of each side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of each side.

    Given that the perimeter is 40m, we can set up the equation:

    4s = 40

    To solve for s, we can divide both sides by 4:

    s = 10

    Therefore, the length of each side of the square is 10m.

Expected answer: 10

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 344m. What is the length of each side of the square?

Gemma 2B:

      To find the length of each side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of each side.

    Given that the perimeter is 344m, we can set up the equation:

    344 = 4s

    To solve for s, we can divide both sides by 4:

    86 = s

    Therefore, the length of each side of the square is 86m.

Expected answer: 86

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 348m. What would be the length of each side of the square?

Gemma 2B:

      To find the length of each side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of each side.

    Given that the perimeter of the square is 348m, we can set up the equation:

    348 = 4s

    To solve for s, we can divide both sides of the equation by 4:

    87 = s

    Therefore, the length of each side of the square is 87m.

Expected answer: 87

Correct? Yes

🔗 Problem

Problem: A rectangle has a perimeter of 194 cm. The length of one of its sides is 49 cm. Can you determine the length of its other side?

Gemma 2B:

      Yes, I can determine the length of the other side.

    Let's call the length of the side that is 49 cm "a". Then, the length of the other side is "b".

    We know that the perimeter of the rectangle is 194 cm, so we can set up the equation:

    a + b + a + b = 194

    Combine like terms:

    2a + 2b = 194

    Subtract a from both sides:

    2a + b = 194 - a

    Subtract b from both sides:

    2a = 194 - a - b

    Divide both sides by 2:

    a = 97 - (a + b)/2

    Now, we need to find the value of a. We can do this by substituting the value of b.

    We know that the length of one side is 49 cm, so we can substitute this value into the equation:

    a = 97 - (49 + b)/2

    Now, we need to solve for b. We can do this by using the equation:

    b = 97 - (49 + b)/2

    We can simplify this equation by combining like terms:

    b = 97 - 49 - b/2

    Subtract b/2 from both sides:

    b/2 = 97 - 49 - b

    Subtract 49 from both sides:

    b/2 = 97 - b

    Subtract b from both sides:

    b/2 = 97 - 2b

    Multiply both sides by 2:

    b = 194 - 2b

    Subtract 2b from both sides:

    b = 194 - 4b

    Now, we can solve for b by dividing both sides by 4:

    b = 194/4

    b = 48

    Now that we have found the value of b, we can find the value of a. We can do this by substituting the value of b into the equation:

    a = 97 - (49 + 48)/2

    a = 97 - 97

    a = 0

    Therefore, the length of the other side of the rectangle is 48 cm.

Expected answer: 48

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 192m. What is the length of one side?

Gemma 2B:

      To find the length of one side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of one side.

    Given that the perimeter is 192m, we can set up the equation:

    192 = 4s

    To solve for s, we can divide both sides by 4:

    48 = s

    Therefore, the length of one side of the square is 48 meters.

Expected answer: 48

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 68cm. What is the length of one side?

Gemma 2B:

      To find the length of one side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of one side.

    Given that the perimeter is 68cm, we can set up the equation:

    68 = 4s

    To solve for s, we can divide both sides by 4:

    68/4 = s

    s = 17

    Therefore, the length of one side of the square is 17cm.

Expected answer: 17

Correct? Yes

🔗 Problem

Problem: A rectangle has a perimeter of 52 meters. If one of the sides measures 4 meters, how long is the other side?

Gemma 2B:

      Let's call the length of the other side x.

    We know that the perimeter of a rectangle is equal to the sum of the lengths of all its sides. In this case, we are given that the perimeter is 52 meters, and we know that one side measures 4 meters.

    So, we can set up the equation:

    4 + x + x + 4 = 52

    Simplifying the equation:

    2x + 8 = 52

    Subtracting 8 from both sides:

    2x = 44

    Dividing both sides by 2:

    x = 22

    So, the other side of the rectangle measures 22 meters.

Expected answer: 22

Correct? Yes

🔗 Problem

Problem: A quadrilateral has a perimeter of 229m. Two sides of the quadrilateral have lengths of 93m and 98m respectively. The third side of the quadrilateral is 36m long. What is the length of the fourth side?

Gemma 2B:

      Let's call the length of the fourth side x.

    We know that the perimeter of the quadrilateral is 229m, so we can set up the equation:

    93 + 98 + 36 + x = 229

    Simplifying the equation:

    93 + 98 + 36 = 229 - x

    137 = 229 - x

    Subtracting 137 from both sides:

    x = 92

    So, the length of the fourth side is 92m.

Expected answer: 2

Correct? No

🔗 Problem

Problem: The perimeter of a square is 16m. What is the length of each side of this square?

Gemma 2B:

      To find the length of each side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of each side.

    Given that the perimeter is 16m, we can set up the equation:

    16 = 4s

    To solve for s, we can divide both sides by 4:

    s = 16/4

    s = 4

    Therefore, the length of each side of the square is 4 meters.

Expected answer: 4

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 272m. What is the length of each side of the square?

Gemma 2B:

      To find the length of each side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of each side.

    Given that the perimeter is 272m, we can set up the equation:

    272 = 4s

    To solve for s, we can divide both sides by 4:

    68 = s

    Therefore, the length of each side of the square is 68m.

Expected answer: 68

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 244m. What is the length of each side of the square?

Gemma 2B:

      To find the length of each side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of each side.

    Given that the perimeter is 244m, we can set up the equation:

    244 = 4s

    To solve for s, we can divide both sides by 4:

    61 = s

    Therefore, the length of each side of the square is 61m.

Expected answer: 61

Correct? Yes

🔗 Problem

Problem: A quadrilateral has a perimeter of 227m. The lengths of three of its sides are 70m, 29m, and 61m. What is the length of the fourth side of the quadrilateral?

Gemma 2B:

      Let's call the length of the fourth side x.

    We know that the perimeter of the quadrilateral is 227m, so we can set up the equation:

    70 + 29 + 61 + x = 227

    Simplifying the equation:

    x = 227 - 70 - 29 - 61

    x = 107

    Therefore, the length of the fourth side of the quadrilateral is 107m.

Expected answer: 67

Correct? No

🔗 Problem

Problem: A square has a perimeter of 280m. What is the length of the side of that square?

Gemma 2B:

      To find the length of the side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of the side.

    Given that the perimeter is 280m, we can set up the equation:

    280 = 4s

    To solve for s, we can divide both sides by 4:

    280/4 = s

    s = 70

    Therefore, the length of the side of the square is 70m.

Expected answer: 70

Correct? Yes

🔗 Problem

Problem: A quadrilateral has a perimeter of 219cm. Two of its sides have lengths of 37cm and 98cm, and a third side is known to be 41cm. How long is the fourth side?

Gemma 2B:

      Let's call the length of the fourth side x.

    We know that the perimeter of a quadrilateral is equal to the sum of the lengths of all its sides. In this case, the perimeter is 219cm, and we know that two of the sides have lengths of 37cm and 98cm. So, we can set up the following equation:

    37 + 98 + x + x = 219

    Simplifying the equation:

    135 + 2x = 219

    Subtracting 135 from both sides:

    2x = 84

    Dividing both sides by 2:

    x = 42

    So, the length of the fourth side is 42cm.

Expected answer: 43

Correct? No

🔗 Problem

Problem: A square has a perimeter of 44m. Can you calculate the length of one side?

Gemma 2B:

      Yes, I can calculate the length of one side of the square.

    The perimeter of a square is equal to the sum of the lengths of all its sides. Since the perimeter of this square is 44 meters, we can set up the following equation:

    4s = 44

    Where s is the length of one side.

    Solving for s, we get:

    s = 44/4

    s = 11

    Therefore, the length of one side of the square is 11 meters.

Expected answer: 11

Correct? Yes

🔗 Problem

Problem: A rectangular garden has a perimeter of 282 meters. The longer side measures 71 meters. What is the length of the shorter side?

Gemma 2B:

      Let's start by using the formula for the perimeter of a rectangle: P = 2(l + w), where l is the length and w is the width.

    We know that the perimeter of the garden is 282 meters, so we can set up an equation:

    2(l + w) = 282

    Simplifying the equation:

    l + w = 141

    We also know that the longer side measures 71 meters, so we can substitute that into the equation:

    71 + w = 141

    Subtracting 71 from both sides:

    w = 70

    So the length of the shorter side is 70 meters.

Expected answer: 70

Correct? Yes

🔗 Problem

Problem: A rectangular garden has a total perimeter of 128 meters. If the shorter side of the garden has a length of 57 meters, how long is the other side?

Gemma 2B:

      Let's call the length of the longer side x.

    The perimeter of the garden is the sum of the lengths of all four sides. Since the shorter side has a length of 57 meters, the longer side must have a length of x - 57 meters.

    The perimeter of the garden is given as 128 meters, so we can set up the equation:

    x - 57 + x + 57 = 128

    Combine like terms:

    2x = 128

    Divide both sides by 2:

    x = 64

    So, the longer side of the garden is 64 meters long.

Expected answer: 7

Correct? No

🔗 Problem

Problem: A square has a perimeter of 392m. What is the length of each side of the square?

Gemma 2B:

      To find the length of each side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of each side.

    Given that the perimeter of the square is 392m, we can set up the equation:

    392 = 4s

    To solve for s, we can divide both sides of the equation by 4:

    98 = s

    Therefore, the length of each side of the square is 98m.

Expected answer: 98

Correct? Yes

🔗 Problem

Problem: A rectangle has a perimeter of 204m. If one of its sides has a length of 16m, what is the length of the other side?

Gemma 2B:

      Let's call the length of the other side x.

    We know that the perimeter of a rectangle is equal to the sum of the lengths of all its sides. In this case, we know that one side has a length of 16m, so we can write:

    Perimeter = 2(16) + 2x

    We are also given that the perimeter is equal to 204m, so we can set up the equation:

    2(16) + 2x = 204

    Simplifying the equation, we get:

    32 + 2x = 204

    Subtracting 32 from both sides, we get:

    2x = 172

    Dividing both sides by 2, we get:

    x = 86

    Therefore, the length of the other side of the rectangle is 86m.

Expected answer: 86

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 336cm. What is the length of one of its sides?

Gemma 2B:

      To find the length of one side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of one side.

    Given that the perimeter is 336cm, we can set up the equation:

    336 = 4s

    To solve for s, we can divide both sides by 4:

    84 = s

    Therefore, the length of one side of the square is 84cm.

Expected answer: 84

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 144 meters. What is the length of one side of the square?

Gemma 2B:

      To find the length of one side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of one side.

    Given that the perimeter is 144 meters, we can set up the equation:

    144 = 4s

    To solve for s, we can divide both sides by 4:

    s = 144/4

    s = 36

    Therefore, the length of one side of the square is 36 meters.

Expected answer: 36

Correct? Yes

🔗 Problem

Problem: A quadrilateral has a perimeter of 236 cm. Two of its sides measure 69 cm and 50 cm respectively, and a third side measures 39 cm. What is the length of the fourth side?

Gemma 2B:

      Let's call the length of the fourth side x.

    We know that the perimeter of a quadrilateral is equal to the sum of the lengths of all its sides. In this case, the perimeter is 236 cm, and we know that two of the sides have lengths of 69 cm and 50 cm, respectively. So, we can set up the following equation:

    69 + 50 + x + 39 = 236

    Simplifying the equation:

    119 + x = 236

    Subtracting 119 from both sides:

    x = 117

    So, the length of the fourth side is 117 cm.

Expected answer: 78

Correct? No

🔗 Problem

Problem: A quadrilateral has a perimeter of 193cm. Two of its sides measure 37cm and 14cm, while the other two sides measure 73cm and an unknown length. What is the length of the side of the quadrilateral that is unknown?

Gemma 2B:

      Let's call the unknown side "x".

    We know that the perimeter of the quadrilateral is 193cm, so we can set up the equation:

    37 + 14 + 73 + x = 193

    Simplifying the equation:

    124 + x = 193

    Subtracting 124 from both sides:

    x = 69

    So, the length of the side of the quadrilateral that is unknown is 69cm.

Expected answer: 69

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 160m. What is the length of one of its sides?

Gemma 2B:

      To find the length of one side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of one side.

    Given that the perimeter is 160m, we can set up the equation:

    160 = 4s

    To solve for s, we can divide both sides by 4:

    40 = s

    Therefore, the length of one side of the square is 40m.

Expected answer: 40

Correct? Yes

🔗 Problem

Problem: A rectangle has a perimeter of 228 meters. The length of the rectangle is 90 meters. What is the width of the rectangle?

Gemma 2B:

      Let's start by using the formula for the perimeter of a rectangle, which is:

    Perimeter = 2(l + w)

    where l is the length and w is the width.

    We know that the perimeter of the rectangle is 228 meters, so we can set up an equation:

    2(90 + w) = 228

    Simplifying the equation:

    180 + w = 114

    Subtracting 180 from both sides:

    w = 34

    Therefore, the width of the rectangle is 34 meters.

Expected answer: 24

Correct? No

🔗 Problem

Problem: The perimeter of a square field is 136 meters. Given that all sides are equal in a square, What is the length of one side of the field?

Gemma 2B:

      To find the length of one side of the square field, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of one side.

    Given that the perimeter of the square field is 136 meters, we can set up the equation:

    136 = 4s

    To solve for s, we can divide both sides by 4:

    s = 136 / 4

    s = 34

    Therefore, the length of one side of the square field is 34 meters.

Expected answer: 34

Correct? Yes

🔗 Problem

Problem: A rectangle has a total perimeter of 236 meters. If one side of the rectangle is 43 meters, can you determine the length of the opposite side?

Gemma 2B:

      Yes, I can determine the length of the opposite side.

    Let's call the length of the side that is 43 meters "a". Then, the length of the opposite side is also "a".

    The perimeter of a rectangle is calculated by adding the lengths of all four sides. Since the total perimeter is 236 meters, we can set up the following equation:

    4a + 4a = 236

    Simplifying the equation:

    8a = 236

    Dividing both sides by 8:

    a = 31

    So, the length of the opposite side is 31 meters.

Expected answer: 75

Correct? No

🔗 Problem

Problem: A quadrilateral has a perimeter of 206m. Two of its sides together have a length of 58m, and the other two sides together have a length of 54m and 1m, respectively. What is the length of the missing portion of the perimeter?

Gemma 2B:

      Let's call the length of the missing portion of the perimeter x.

    We know that the perimeter of the quadrilateral is 206m, so we can set up the equation:

    58 + 54 + 1 + x = 206

    Simplifying the equation:

    113 + x = 206

    Subtracting 113 from both sides:

    x = 93

    Therefore, the length of the missing portion of the perimeter is 93m.

Expected answer: 93

Correct? Yes

🔗 Problem

Problem: A square field has a total perimeter of 284 meters. How long is each side of the square field?

Gemma 2B:

      To find the length of each side of the square field, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of each side.

    Given that the perimeter of the square field is 284 meters, we can set up the equation:

    284 = 4s

    To solve for s, we can divide both sides of the equation by 4:

    284/4 = s

    s = 71 meters

    Therefore, each side of the square field is 71 meters long.

Expected answer: 71

Correct? Yes

🔗 Problem

Problem: A rectangle has a perimeter of 150 feet. If the length of the rectangle is 69 feet, what is the width of the rectangle?

Gemma 2B:

      To find the width of the rectangle, we can use the formula:

    Perimeter = 2(l + w)

    where l is the length and w is the width.

    Given that the perimeter is 150 feet and the length is 69 feet, we can set up the equation:

    150 = 2(69 + w)

    Simplifying the equation:

    150 = 138 + 2w

    Subtracting 138 from both sides:

    12 = 2w

    Dividing both sides by 2:

    6 = w

    Therefore, the width of the rectangle is 6 feet.

Expected answer: 6

Correct? Yes

🔗 Problem

Problem: The perimeter of a rectangle is 166m. If one of the sides measures 35m, how long is the other side?

Gemma 2B:

      Let's call the other side x.

    We know that the perimeter of a rectangle is equal to the sum of the lengths of all its sides. In this case, we are given that the perimeter is 166m, and we know that one side is 35m.

    So, we can set up the equation:

    35 + x + 35 + x = 166

    Simplifying the equation:

    2x + 70 = 166

    Subtracting 70 from both sides:

    2x = 96

    Dividing both sides by 2:

    x = 48

    Therefore, the other side of the rectangle is 48m.

Expected answer: 48

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 124m. What is the length of each side?

Gemma 2B:

      To find the length of each side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of each side.

    Given that the perimeter is 124m, we can set up the equation:

    124 = 4s

    To solve for s, we can divide both sides by 4:

    31 = s

    Therefore, the length of each side of the square is 31 meters.

Expected answer: 31

Correct? Yes

🔗 Problem

Problem: A rectangular field has a perimeter of 336 feet. The length of one of its sides is 79 feet. What is the length of the opposite side?

Gemma 2B:

      Let's call the length of the opposite side x.

    We know that the perimeter of a rectangle is equal to the sum of the lengths of all its sides. In this case, the perimeter is 336 feet, and we know that one side is 79 feet long.

    So, we can set up the equation:

    79 + x + x + 79 = 336

    Simplifying the equation:

    2x + 158 = 336

    Subtracting 158 from both sides:

    2x = 178

    Dividing both sides by 2:

    x = 89

    Therefore, the length of the opposite side is 89 feet.

Expected answer: 89

Correct? Yes

🔗 Problem

Problem: A square plot of land has a perimeter of 132 meters. What is the length of one side of the square?

Gemma 2B:

      To find the length of one side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of one side.

    Given that the perimeter is 132 meters, we can set up the equation:

    132 = 4s

    To solve for s, we can divide both sides by 4:

    33 = s

    Therefore, the length of one side of the square is 33 meters.

Expected answer: 33

Correct? Yes

🔗 Problem

Problem: A rectangle has a perimeter of 138 feet. If the length of the rectangle is 46 feet, what is the width of the rectangle?

Gemma 2B:

      Let's start by using the formula for the perimeter of a rectangle, which is P = 2(l + w), where l is the length and w is the width.

    We know that the perimeter of the rectangle is 138 feet, so we can set up an equation using this information:

    P = 2(l + w)
    138 = 2(46 + w)

    Now, we can solve for w by dividing both sides of the equation by 2:

    w = (138 - 2(46)) / 2
    w = (138 - 92) / 2
    w = 46 / 2
    w = 23

    So, the width of the rectangle is 23 feet.

Expected answer: 23

Correct? Yes

🔗 Problem

Problem: A rectangular field has a total perimeter of 200 meters. The length of the field is known to be 49 meters. What is the width of the field in meters?

Gemma 2B:

      Let's start by using the formula for the perimeter of a rectangle, which is:

    Perimeter = 2(l + w)

    where l is the length and w is the width.

    We know that the perimeter of the field is 200 meters, so we can set up an equation using this information:

    2(49 + w) = 200

    Simplifying this equation, we get:

    98 + w = 100

    Subtracting 98 from both sides, we get:

    w = 2

    Therefore, the width of the field is 2 meters.

Expected answer: 51

Correct? No

🔗 Problem

Problem: A square has a perimeter of 200m. What is the length of each side?

Gemma 2B:

      To find the length of each side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of each side.

    Given that the perimeter is 200m, we can set up the equation:

    200 = 4s

    To solve for s, we can divide both sides by 4:

    50 = s

    Therefore, the length of each side of the square is 50m.

Expected answer: 50

Correct? Yes

🔗 Problem

Problem: A quadrilateral has a perimeter of 199m. The length of one side is 9m, the length of the second side is 30m, and the length of the third side is 71m. What is the length of the fourth side?

Gemma 2B:

      Let's call the length of the fourth side x.

    We know that the perimeter of a quadrilateral is equal to the sum of the lengths of all its sides. In this case, the perimeter is 199m, so we can set up the equation:

    9 + 30 + 71 + x = 199

    Simplifying the equation:

    x = 199 - 9 - 30 - 71

    x = 99

    Therefore, the length of the fourth side is 99m.

Expected answer: 89

Correct? No

🔗 Problem

Problem: A quadrilateral has a perimeter of 207m. The lengths of three of its sides are 35m, 62m and 70m respectively. What is the length of the fourth side?

Gemma 2B:

      Let's call the length of the fourth side x.

    We know that the perimeter of a quadrilateral is equal to the sum of the lengths of all its sides. In this case, the perimeter is 207m, and we know the lengths of three of the sides: 35m, 62m, and 70m.

    So, we can set up the following equation:

    35 + 62 + 70 + x = 207

    Simplifying the equation:

    167 + x = 207

    Subtracting 167 from both sides:

    x = 40

    Therefore, the length of the fourth side is 40m.

Expected answer: 40

Correct? Yes

🔗 Problem

Problem: A rectangle has a perimeter of 384cm. If one of the shorter sides of the rectangle is measured to be 99cm, what would be the length of the longer sides of the rectangle?

Gemma 2B:

      Let's call the length of the longer sides of the rectangle "x" cm.

    We know that the perimeter of the rectangle is 384 cm, so we can set up the equation:

    2(x + 99) = 384

    Simplifying the equation:

    2x + 198 = 384

    Subtracting 198 from both sides:

    2x = 186

    Dividing both sides by 2:

    x = 93

    So, the length of the longer sides of the rectangle is 93 cm.

Expected answer: 93

Correct? Yes

🔗 Problem

Problem: A quadrilateral shape has a perimeter of 255 m. The first and the second sides have lengths of 78m and 15m respectively, while the third side has a length of 63m. What is the length of the fourth side?

Gemma 2B:

      Let's call the length of the fourth side x.

    We know that the perimeter of a quadrilateral is equal to the sum of the lengths of all its sides. In this case, the perimeter is 255 m, so we can set up the equation:

    78 + 15 + 63 + x = 255

    Simplifying the equation:

    96 + x = 255

    Subtracting 96 from both sides:

    x = 159

    Therefore, the length of the fourth side is 159 m.

Expected answer: 99

Correct? No

🔗 Problem

Problem: A square has a perimeter of 128m. What is the length of one of its sides?

Gemma 2B:

      To find the length of one side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of one side.

    Given that the perimeter is 128m, we can set up the equation:

    128 = 4s

    To solve for s, we can divide both sides by 4:

    32 = s

    Therefore, the length of one side of the square is 32 meters.

Expected answer: 32

Correct? Yes

🔗 Problem

Problem: Imagine a rectangle with a perimeter of 96 feet. You know that one pair of opposite sides are each 33 feet long. Can you find the length of the other pair of opposite sides?

Gemma 2B:

      Yes, I can find the length of the other pair of opposite sides.

    Let's call the length of the longer side x. Then the length of the shorter side is 96 - x.

    We know that the perimeter of the rectangle is 96 feet, so we can set up the equation:

    2x + (96 - x) = 96

    Simplifying the equation:

    2x + 96 - x = 96

    Combine like terms:

    3x = 96

    Divide both sides by 3:

    x = 32

    So the length of the longer side is 32 feet. The length of the shorter side is 96 - 32 = 64 feet.

Expected answer: 15

Correct? No

🔗 Problem

Problem: The perimeter of a square field is 112 meters. What is the length of each side?

Gemma 2B:

      To find the length of each side of the square field, we can use the formula:

    Perimeter = 4 x side length

    Since the perimeter is given as 112 meters, we can set up the equation:

    112 = 4 x side length

    To solve for the side length, we can divide both sides of the equation by 4:

    side length = 112 / 4

    side length = 28 meters

    Therefore, the length of each side of the square field is 28 meters.

Expected answer: 28

Correct? Yes

🔗 Problem

Problem: The perimeter of a square is 32 cm. Can you find the length of one of its sides?

Gemma 2B:

      Yes, I can find the length of one of the sides of the square.

    The perimeter of a square is equal to the sum of the lengths of all its sides. Since the perimeter of this square is 32 cm, we can set up the equation:

    4s = 32

    where s is the length of one side.

    To solve for s, we can divide both sides of the equation by 4:

    s = 32/4

    s = 8

    Therefore, the length of one side of the square is 8 cm.

Expected answer: 8

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 364m. What is the length of each side of the square?

Gemma 2B:

      To find the length of each side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of each side.

    Given that the perimeter of the square is 364m, we can set up the equation:

    364 = 4s

    To solve for s, we can divide both sides of the equation by 4:

    91 = s

    Therefore, the length of each side of the square is 91 meters.

Expected answer: 91

Correct? Yes

🔗 Problem

Problem: The total perimeter of a rectangle is found to be 144 feet. The length of one side is known to be 38 feet. What is the length of the other side of the rectangle in feet?

Gemma 2B:

      Let's call the length of the other side x.

    We know that the perimeter of a rectangle is equal to the sum of the lengths of all four sides. In this case, we are given that the perimeter is 144 feet, and we know that one side is 38 feet long.

    So, we can set up the equation:

    38 + x + 38 + x = 144

    Simplifying the equation:

    2x + 76 = 144

    Subtracting 76 from both sides:

    2x = 68

    Dividing both sides by 2:

    x = 34

    Therefore, the length of the other side of the rectangle is 34 feet.

Expected answer: 34

Correct? Yes

🔗 Problem

Problem: A quadrilateral has a perimeter of 205m. Two of its sides add up to 54m and the other two sides add up to 22m and 37m respectively. What is the length of the remaining side to complete the perimeter?

Gemma 2B:

      Let's call the length of the remaining side x.

    We know that the perimeter of the quadrilateral is 205m, so we can set up the equation:

    54 + 22 + 37 + x = 205

    Simplifying the equation:

    x = 205 - 54 - 22 - 37

    x = 112

    Therefore, the length of the remaining side to complete the perimeter is 112m.

Expected answer: 92

Correct? No

🔗 Problem

Problem: The perimeter of a rectangular field is 174m. If the length of the field is 65m, what is the width of the field?

Gemma 2B:

      To find the width of the field, we can use the formula for the perimeter of a rectangle, which is:

    Perimeter = 2(l + w)

    where l is the length and w is the width of the rectangle.

    Given that the perimeter of the field is 174m and the length is 65m, we can set up the equation:

    2(65 + w) = 174

    Simplifying the equation:

    2(65) + 2w = 174

    130 + 2w = 174

    2w = 44

    w = 22

    Therefore, the width of the field is 22m.

Expected answer: 22

Correct? Yes

🔗 Problem

Problem: A quadrilateral has a perimeter of 176 cm. The lengths of three sides are 25 cm, 17 cm and 89 cm respectively. What is the length of the fourth side?

Gemma 2B:

      Let's call the length of the fourth side x.

    We know that the perimeter of a quadrilateral is equal to the sum of the lengths of all its sides. So, we can set up the equation:

    25 + 17 + 89 + x = 176

    Simplifying the equation:

    121 + x = 176

    Subtracting 121 from both sides:

    x = 55

    Therefore, the length of the fourth side is 55 cm.

Expected answer: 45

Correct? No

🔗 Problem

Problem: A square has a perimeter of 372 meters. What is the length of each side?

Gemma 2B:

      To find the length of each side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of each side.

    Given that the perimeter is 372 meters, we can set up the equation:

    372 = 4s

    To solve for s, we can divide both sides by 4:

    93 = s

    Therefore, the length of each side of the square is 93 meters.

Expected answer: 93

Correct? Yes

🔗 Problem

Problem: A square field has a perimeter of 240 meters. Can you find out the length of one side of the field?

Gemma 2B:

      Yes, I can help you with that!

    The perimeter of a square is equal to the sum of the lengths of all its sides. Since the perimeter of the square field is 240 meters, we can set up the following equation:

    4s = 240

    where s is the length of one side of the square.

    To solve for s, we can divide both sides of the equation by 4:

    s = 240 / 4

    s = 60 meters

    Therefore, the length of one side of the square field is 60 meters.

Expected answer: 60

Correct? Yes

🔗 Problem

Problem: The perimeter of a rectangle is 242 meters. Knowing that one of the sides of this rectangle is 97 meters, can you determine the length of the other side?

Gemma 2B:

      Yes, I can determine the length of the other side.

    Let's call the length of the side that is 97 meters "a". Then, the other side must be "b".

    We know that the perimeter of the rectangle is 242 meters, so we can set up the equation:

    a + b + a + b = 242

    Combine like terms:

    2a + 2b = 242

    Subtract 2a from both sides:

    2b = 242 - 2a

    Subtract 2a from both sides:

    2b = 242 - 2(97)

    2b = 242 - 194

    2b = 48

    Divide both sides by 2:

    b = 48/2

    b = 24

    So, the length of the other side is 24 meters.

Expected answer: 24

Correct? Yes

🔗 Problem

Problem: Tom has constructed a square with a total perimeter of 316 meters. Can you determine the length of each side of this square?

Gemma 2B:

      Yes, I can determine the length of each side of the square.

    Let's start by using the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of each side.

    We know that the perimeter of the square is 316 meters, so we can set up an equation:

    4s = 316

    To solve for s, we can divide both sides by 4:

    s = 316/4

    s = 79 meters

    So, the length of each side of the square is 79 meters.

Expected answer: 79

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 268cm. What is the length of each side of the square?

Gemma 2B:

      Reasoning: The perimeter of a square is equal to the sum of the lengths of all its sides.
    Let's call the length of each side of the square "x".
    Then, the perimeter of the square is equal to 4x.
    Given that the perimeter of the square is 268cm, we can set up the equation:
    4x = 268
    To solve for x, we can divide both sides of the equation by 4:
    x = 268/4
    x = <<268/4=67>>67
    So, the length of each side of the square is 67cm.
    ### Answer: 67

Expected answer: 67

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 348m. What is the length of each side of the square?

Gemma 2B:

      To find the length of each side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of each side.

    Given that the perimeter is 348m, we can set up the equation:

    348 = 4s

    To solve for s, we can divide both sides by 4:

    87 = s

    Therefore, the length of each side of the square is 87m.

Expected answer: 87

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 400m. What is the length of one of its sides?

Gemma 2B:

      To find the length of one side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of one side.

    Given that the perimeter is 400m, we can set up the equation:

    400 = 4s

    To solve for s, we can divide both sides by 4:

    100 = s

    Therefore, the length of one side of the square is 100m.

Expected answer: 100

Correct? Yes

🔗 Problem

Problem: A quadrilateral has sides with lengths of 81m, 100m, and 19m. If its perimeter is 243m, what is the length of the fourth side?

Gemma 2B:

      Let's call the length of the fourth side x.

    We know that the perimeter of a quadrilateral is the sum of the lengths of all its sides. In this case, the perimeter is 243m.

    We can set up an equation using the information given:

    81 + 100 + 19 + x = 243

    Simplifying the equation:

    199 + x = 243

    Subtracting 199 from both sides:

    x = 44

    So, the length of the fourth side is 44m.

Expected answer: 43

Correct? No

🔗 Problem

Problem: A rectangle has a perimeter of 186cm. If one of its sides is 50cm long, how long is the other side?

Gemma 2B:

      Let's call the length of the other side x.

    We know that the perimeter of a rectangle is equal to the sum of the lengths of all its sides. In this case, we are given that one side is 50cm long, so the perimeter is equal to 50 + x + x + 50 = 186.

    Simplifying this equation, we get 2x + 100 = 186.

    Subtracting 100 from both sides gives us 2x = 86.

    Dividing both sides by 2 gives us x = 43.

    So, the length of the other side is 43cm.

Expected answer: 43

Correct? Yes

🔗 Problem

Problem: A rectangle has a perimeter of 224 cm. If the length of one of its sides is 78 cm, what is the length of the adjacent side?

Gemma 2B:

      Let's call the length of the adjacent side x.

    We know that the perimeter of a rectangle is equal to the sum of the lengths of all its sides. In this case, the perimeter is 224 cm, and we know that one side is 78 cm long.

    So, we can set up the following equation:

    78 + x + x + 78 = 224

    Simplifying the equation:

    2x + 156 = 224

    Subtracting 156 from both sides:

    2x = 68

    Dividing both sides by 2:

    x = 34

    Therefore, the length of the adjacent side is 34 cm.

Expected answer: 34

Correct? Yes

🔗 Problem

Problem: A quadrilateral has two sides measuring 79m and 97m. Another side measures 51m. The total perimeter of the quadrilateral is 235m. What is the length of the fourth side?

Gemma 2B:

      Let's call the length of the fourth side x.

    We know that the sum of the lengths of all four sides of a quadrilateral is equal to the perimeter of the quadrilateral. So, we can set up the equation:

    79 + 97 + 51 + x = 235

    Simplifying the equation:

    227 + x = 235

    Subtracting 227 from both sides:

    x = 8

    So, the length of the fourth side is 8 meters.

Expected answer: 8

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 28m. Can you calculate the length of one side of this square?

Gemma 2B:

      Yes, I can calculate the length of one side of the square.

    The perimeter of a square is equal to the sum of the lengths of all its sides. Since the perimeter of this square is 28 meters, we can set up the following equation:

    4s = 28

    where s is the length of one side of the square.

    To solve for s, we can divide both sides of the equation by 4:

    s = 28/4

    s = 7

    Therefore, the length of one side of the square is 7 meters.

Expected answer: 7

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 48cm. What is the length of each side?

Gemma 2B:

      Reasoning: The perimeter of a square is equal to the sum of the lengths of all its sides. Since the perimeter of this square is 48cm, we can set up the equation:

    4s = 48

    where s is the length of each side.

    Solving for s, we get:

    s = 48/4

    s = <<48/4=12>>12

    Therefore, the length of each side of the square is 12cm.
    ### Answer: 12

Expected answer: 12

Correct? Yes

🔗 Problem

Problem: A square plot of land has a perimeter of 184 meters. Can you find the length of one side of the plot?

Gemma 2B:

      Yes, I can help you with that.

    The perimeter of a square is equal to the sum of the lengths of all its sides. Since the perimeter of the square plot of land is given as 184 meters, we can set up the following equation:

    4s = 184

    where s is the length of one side of the square.

    To solve for s, we can divide both sides of the equation by 4:

    s = 184/4

    s = 46 meters

    Therefore, the length of one side of the square plot of land is 46 meters.

Expected answer: 46

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 56 meters. What is the length of each side?

Gemma 2B:

      To find the length of each side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of each side.

    Given that the perimeter is 56 meters, we can set up the equation:

    56 = 4s

    To solve for s, we can divide both sides by 4:

    56/4 = s

    s = 14 meters

    Therefore, the length of each side of the square is 14 meters.

Expected answer: 14

Correct? Yes

🔗 Problem

Problem: A quadrilateral has a perimeter of 157m. If one of its sides is 97m long, and the other two sides are 5m and 30m, respectively, what is the length of the fourth side to complete the perimeter?

Gemma 2B:

      Let's call the length of the fourth side x.

    We know that the perimeter of a quadrilateral is the sum of the lengths of all its sides. In this case, the perimeter is 157m, and we know that one side is 97m long, so we can write an equation:

    97 + 5 + 30 + x = 157

    Simplifying the equation:

    97 + 35 + x = 157

    Subtracting 35 from both sides:

    62 + x = 122

    Subtracting 62 from both sides:

    x = 60

    So, the length of the fourth side to complete the perimeter is 60m.

Expected answer: 25

Correct? No

🔗 Problem

Problem: A quadrilateral has a perimeter of 173m. The length of the first side is 46m, second side is 50m and third side is 35m. What is the length of the fourth side?

Gemma 2B:

      Let's call the length of the fourth side x.

    We know that the perimeter of a quadrilateral is equal to the sum of the lengths of all its sides. In this case, the perimeter is 173m, so we can set up the equation:

    46 + 50 + 35 + x = 173

    Simplifying the equation:

    131 + x = 173

    Subtracting 131 from both sides:

    x = 42

    So, the length of the fourth side is 42m.

Expected answer: 42

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 72 cm. What is the length of one of its sides?

Gemma 2B:

      To find the length of one side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of one side.

    Given that the perimeter is 72 cm, we can set up the equation:

    4s = 72

    To solve for s, we can divide both sides by 4:

    s = 72/4

    s = 18

    Therefore, the length of one side of the square is 18 cm.

Expected answer: 18

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 352m. What is the length of each side of the square?

Gemma 2B:

      To find the length of each side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of each side.

    Given that the perimeter is 352m, we can set up the equation:

    352 = 4s

    To solve for s, we can divide both sides by 4:

    88 = s

    Therefore, the length of each side of the square is 88m.

Expected answer: 88

Correct? Yes

🔗 Problem

Problem: A rectangle has 23m for its length and has a total perimeter of 116m. What is the length of its width?

Gemma 2B:

      Let's start by using the formula for the perimeter of a rectangle, which is:

    Perimeter = 2(l + w)

    where l is the length and w is the width.

    We know that the length of the rectangle is 23m, so we can substitute this value into the formula:

    Perimeter = 2(23 + w)

    We also know that the perimeter of the rectangle is 116m, so we can set up an equation:

    2(23 + w) = 116

    Now we can solve for w:

    23 + w = 58

    w = 58 - 23

    w = 35

    So the width of the rectangle is 35m.

Expected answer: 35

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 124m. What is the length of each side?

Gemma 2B:

      To find the length of each side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of each side.

    Given that the perimeter is 124m, we can set up the equation:

    124 = 4s

    To solve for s, we can divide both sides by 4:

    31 = s

    Therefore, the length of each side of the square is 31 meters.

Expected answer: 31

Correct? Yes

🔗 Problem

Problem: A quadrilateral has a total perimeter of 131m. Three of its sides have lengths 24m, 57m, and 17m respectively. What is the length of the fourth side?

Gemma 2B:

      Let's call the length of the fourth side x.

    We know that the perimeter of a quadrilateral is equal to the sum of its sides. So, we can set up the equation:

    24 + 57 + 17 + x = 131

    Simplifying the equation:

    98 + x = 131

    Subtracting 98 from both sides:

    x = 33

    So, the length of the fourth side is 33 meters.

Expected answer: 33

Correct? Yes

🔗 Problem

Problem: A rectangle has a perimeter of 254m. One of its sides has a length of 89m. What is the length of the other side?

Gemma 2B:

      Let's call the length of the other side x.

    We know that the perimeter of a rectangle is equal to the sum of the lengths of all its sides. In this case, we know that one side has a length of 89m, so the perimeter is equal to 89 + x + x + x = 254.

    Simplifying the equation, we get 3x + 89 = 254.

    Solving for x, we get x = 165.

    So, the length of the other side is 165m.

Expected answer: 38

Correct? No

🔗 Problem

Problem: A square has a perimeter of 208m. What is the length of each side?

Gemma 2B:

      To find the length of each side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of each side.

    Given that the perimeter is 208m, we can set up the equation:

    208 = 4s

    To solve for s, we can divide both sides by 4:

    52 = s

    Therefore, the length of each side of the square is 52m.

Expected answer: 52

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 64m. What is the length of each side of the square?

Gemma 2B:

      To find the length of each side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of each side.

    Given that the perimeter is 64m, we can set up the equation:

    64 = 4s

    To solve for s, we can divide both sides by 4:

    16 = s

    Therefore, the length of each side of the square is 16 meters.

Expected answer: 16

Correct? Yes

🔗 Problem

Problem: A quadrilateral has a total perimeter of 196 meters. The lengths of three of its sides combined is 183 meters (with one side being 92 meters and the other two sides being 29 and 62 meters respectively). Can you figure out the length of the fourth side?

Gemma 2B:

      Yes, I can help you with that.

    Let's call the length of the fourth side x.

    We know that the total perimeter of the quadrilateral is 196 meters, so we can set up the equation:

    92 + 29 + 62 + x = 196

    Simplifying the equation:

    x = 196 - 92 - 29 - 62

    x = 125

    So, the length of the fourth side is 125 meters.

Expected answer: 13

Correct? No

🔗 Problem

Problem: The perimeter of a quadrilateral is 191 units. If one side is 35 units in length, another side is 76 units, and the third side is 5 units, what is the length of the fourth side in units?

Gemma 2B:

      Let's call the length of the fourth side x.

    We know that the perimeter of a quadrilateral is equal to the sum of the lengths of all its sides. In this case, the perimeter is 191 units, and we know the lengths of three of the sides: 35, 76, and 5.

    So, we can set up the following equation:

    35 + 76 + 5 + x = 191

    Simplifying the equation:

    116 + x = 191

    Subtracting 116 from both sides:

    x = 75

    Therefore, the length of the fourth side is 75 units.

Expected answer: 75

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 104m. What is the length of each side?

Gemma 2B:

      To find the length of each side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of each side.

    Given that the perimeter is 104m, we can set up the equation:

    104 = 4s

    To solve for s, we can divide both sides by 4:

    26 = s

    Therefore, the length of each side of the square is 26m.

Expected answer: 26

Correct? Yes

🔗 Problem

Problem: The perimeter of a rectangle is 198 cm. If the length of this rectangle is 90 cm, what is the width?

Gemma 2B:

      To find the width of the rectangle, we can use the formula for the perimeter of a rectangle, which is:

    Perimeter = 2(l + w)

    where l is the length and w is the width.

    Given that the perimeter is 198 cm and the length is 90 cm, we can set up the equation:

    2(90 + w) = 198

    Simplifying the equation:

    180 + w = 198

    Subtracting 180 from both sides:

    w = 18

    Therefore, the width of the rectangle is 18 cm.

Expected answer: 9

Correct? No

🔗 Problem

Problem: Jack is designing a rectangular garden with a total perimeter of 128 feet. He has already planned for one pair of opposite sides to be 47 feet each. What should be the length of the remaining two opposite sides?

Gemma 2B:

      Let's call the length of the remaining two opposite sides x.

    We know that the total perimeter of the garden is 128 feet, so we can set up the equation:

    47 + 47 + 2x = 128

    Simplifying the equation:

    2x = 40

    x = 20

    So, the length of the remaining two opposite sides should be 20 feet.

Expected answer: 17

Correct? No

🔗 Problem

Problem: A square has a perimeter of 356m. What is the length of one of its sides?

Gemma 2B:

      To find the length of one side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of one side.

    Given that the perimeter is 356m, we can set up the equation:

    356 = 4s

    To solve for s, we can divide both sides by 4:

    s = 356/4

    s = 89

    Therefore, the length of one side of the square is 89m.

Expected answer: 89

Correct? Yes

🔗 Problem

Problem: A quadrilateral has a perimeter of 236 units. Two sides of the quadrilateral measure 89 units and 87 units respectively, while the third side is 1 unit long. What is the length of the fourth side?

Gemma 2B:

      Let's call the length of the fourth side x.

    We know that the perimeter of the quadrilateral is 236, so we can set up the equation:

    89 + 87 + 1 + x = 236

    Simplifying the equation:

    177 + x = 236

    Subtracting 177 from both sides:

    x = 236 - 177

    x = 59

    Therefore, the length of the fourth side is 59 units.

Expected answer: 59

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 340 meters. What is the length of each side of this square?

Gemma 2B:

      To find the length of each side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of each side.

    Given that the perimeter is 340 meters, we can set up the equation:

    340 = 4s

    To solve for s, we can divide both sides by 4:

    85 = s

    Therefore, the length of each side of the square is 85 meters.

Expected answer: 85

Correct? Yes

🔗 Problem

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

Gemma 2B:

      To find the length of each side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of each side.

    Given that the perimeter is 16m, we can set up the equation:

    16 = 4s

    To solve for s, we can divide both sides by 4:

    s = 16/4

    s = 4

    Therefore, the length of each side of the square is 4 meters.

Expected answer: 4

Correct? Yes

🔗 Problem

Problem: A quadrilateral has four sides. The length of the first side is 1m, the second side is 54m, and the third side is 9m. The total perimeter of this quadrilateral is 81m. What would be the length of the fourth side in meters?

Gemma 2B:

      Let's call the length of the fourth side x.

    We know that the perimeter of a quadrilateral is the sum of the lengths of all its sides. In this case, the perimeter is 81 meters.

    So, we can set up the equation:

    1 + 54 + 9 + x = 81

    Simplifying the equation:

    54 + 9 + x = 81

    Subtracting 54 and 9 from both sides:

    x = 28

    Therefore, the length of the fourth side is 28 meters.

Expected answer: 17

Correct? No

🔗 Problem

Problem: A quadrilateral, which is a perfect square, has a total perimeter of 316m. What is the length of each side of this square?

Gemma 2B:

      To find the length of each side of the square, we can use the formula for the perimeter of a quadrilateral, which is:

    Perimeter = 4s

    where s is the side length.

    Given that the quadrilateral is a perfect square, we know that all sides are equal. Therefore, we can substitute s = 12m (since the perimeter is 316m and there are 4 sides):

    Perimeter = 4s
    Perimeter = 4(12)
    Perimeter = 48

    Therefore, the length of each side of the square is 12m.

Expected answer: 79

Correct? No

🔗 Problem

Problem: A square has a perimeter of 300m. How long is each side of the square?

Gemma 2B:

      To find the length of each side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of each side.

    Given that the perimeter is 300m, we can set up the equation:

    300 = 4s

    To solve for s, we can divide both sides by 4:

    75 = s

    Therefore, each side of the square is 75m long.

Expected answer: 75

Correct? Yes

🔗 Problem

Problem: A quadrilateral has a perimeter of 198m. Two of the sides have lengths of 19m and 57m respectively, another side is 22m, what is the length of the remaining side?

Gemma 2B:

      Let's call the length of the remaining side x.

    We know that the perimeter of a quadrilateral is equal to the sum of the lengths of all its sides. In this case, the perimeter is 198m, and we know that two of the sides have lengths of 19m and 57m, respectively. So, we can set up the following equation:

    19 + 57 + 22 + x = 198

    Simplifying the equation:

    98 + x = 198

    Subtracting 98 from both sides:

    x = 100

    Therefore, the length of the remaining side is 100m.

Expected answer: 100

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 172m. What is the length of each side of the square?

Gemma 2B:

      To find the length of each side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of each side.

    Given that the perimeter is 172m, we can set up the equation:

    172 = 4s

    To solve for s, we can divide both sides by 4:

    43 = s

    Therefore, the length of each side of the square is 43 meters.

Expected answer: 43

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 304 cm. What is the length of one of its sides?

Gemma 2B:

      To find the length of one side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of one side.

    Given that the perimeter is 304 cm, we can set up the equation:

    304 = 4s

    To solve for s, we can divide both sides by 4:

    76 = s

    Therefore, the length of one side of the square is 76 cm.

Expected answer: 76

Correct? Yes

🔗 Problem

Problem: A rectangle has a total perimeter of 158 meters. Each of the shorter sides is 51 meters long. What is the length of each of the longer sides?

Gemma 2B:

      Let's call the length of each longer side "x" meters.

    The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is 158 meters.

    We know that the shorter sides are 51 meters long, so the total length of the shorter sides is 51 + 51 = 102 meters.

    The total length of the longer sides is x + x = 2x meters.

    We can set up the following equation to represent the problem:

    158 = 102 + 2x

    Solving for x, we get:

    x = 56 meters

    So, the length of each of the longer sides is 56 meters.

Expected answer: 28

Correct? No

🔗 Problem

Problem: A square has a perimeter of 72m. What is the length of one its sides?

Gemma 2B:

      To find the length of one side of a square with a perimeter of 72 meters, we can use the formula:

    Perimeter = 4s

    where s is the length of one side.

    We are given that the perimeter is 72 meters, so we can set up the equation:

    72 = 4s

    To solve for s, we can divide both sides by 4:

    18 = s

    Therefore, the length of one side of the square is 18 meters.

Expected answer: 18

Correct? Yes

🔗 Problem

Problem: A rectangular playground is bordered by a fence. Two opposite sides of the fence are 19m each. If the total length of the fence is 166m, what is the length of each of the other two sides?

Gemma 2B:

      Let's call the length of each of the other two sides x.

    We know that the total length of the fence is 166m, so we can set up the equation:

    19m + 19m + 2x = 166m

    Simplifying the equation:

    2x = 148m

    Dividing both sides by 2:

    x = 74m

    So the length of each of the other two sides is 74m.

Expected answer: 64

Correct? No

🔗 Problem

Problem: A quadrilateral has a perimeter of 246m. You know that two of its sides are 40m and 32m long, another side is 95m long. What is the length of the fourth side?

Gemma 2B:

      Let's call the length of the fourth side x.

    We know that the perimeter of a quadrilateral is equal to the sum of the lengths of all its sides. In this case, we know that the perimeter is 246m.

    We also know that two of the sides have lengths of 40m and 32m, and another side has a length of 95m. So, we can set up the following equation:

    40 + 32 + 95 + x = 246

    Simplifying the equation:

    77 + x = 246

    Subtracting 77 from both sides:

    x = 169

    So, the length of the fourth side is 169m.

Expected answer: 79

Correct? No

🔗 Problem

Problem: A square has a perimeter of 32m. What is the length of one of its sides?

Gemma 2B:

      To find the length of one side of the square, we can use the formula for the perimeter of a square, which is:

    Perimeter = 4s

    where s is the length of one side.

    Given that the perimeter is 32m, we can set up the equation:

    32 = 4s

    To solve for s, we can divide both sides by 4:

    8 = s

    Therefore, the length of one side of the square is 8 meters.

Expected answer: 8

Correct? Yes

🔗 Problem

Problem: A square has a perimeter of 12 meters. Can you find the length of one side of the square?

Gemma 2B:

      Yes, I can help you with that!

    The perimeter of a square is equal to the sum of the lengths of all its sides. Since the perimeter of this square is 12 meters, we can set up the following equation:

    4s = 12

    where s is the length of one side of the square.

    To solve for s, we can divide both sides of the equation by 4:

    s = 12/4

    s = 3

    Therefore, the length of one side of the square is 3 meters.

Expected answer: 3

Correct? Yes

🔗 Problem

Problem: A quadrilateral has a perimeter of 160m. If the three known sides have lengths of 29m, 16m, and 41m, what is the length of the fourth side?

Gemma 2B:

      Let's call the length of the fourth side x.

    We know that the perimeter of a quadrilateral is equal to the sum of its sides. So, we can set up the equation:

    29 + 16 + 41 + x = 160

    Simplifying the equation:

    86 + x = 160

    Subtracting 86 from both sides:

    x = 74

    Therefore, the length of the fourth side is 74 meters.

Expected answer: 74

Correct? Yes

🔗 Problem

Problem: A rectangle has a perimeter of 98m. If one of its sides is 5m long, what is the length of the other side?

Gemma 2B:

      Let's call the length of the other side x.

    We know that the perimeter of a rectangle is equal to the sum of the lengths of all its sides. In this case, we know that one side is 5m long, so the perimeter is equal to 5 + x + x + 5 = 98.

    Simplifying this equation, we get 2x + 10 = 98.

    Subtracting 10 from both sides gives us 2x = 88.

    Dividing both sides by 2 gives us x = 44.

    So, the length of the other side is 44m.

Expected answer: 44

Correct? Yes

🔗 Problem

Problem: A rectangle has two sides measuring 45m each. If the total perimeter of the rectangle is 210m, what is the length of each of the other two sides?

Gemma 2B:

      Let's call the length of each of the other two sides x.

    We know that the perimeter of a rectangle is the sum of the lengths of all four sides. In this case, the perimeter is 210m.

    So, we can set up the equation:

    45 + 45 + x + x = 210

    Simplifying the equation:

    90 + x + x = 210

    Combine like terms:

    2x + 90 = 210

    Subtract 90 from both sides:

    2x = 120

    Divide both sides by 2:

    x = 60

    So, the length of each of the other two sides is 60m.

Expected answer: 60

Correct? Yes