🔗 Problem

Problem: An equilateral triangle has a perimeter of 990cm. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 990cm, so we can set up the equation:

    3x = 990

    To solve for x, we can divide both sides of the equation by 3:

    x = 990/3
    x = 330

    So, the length of each side of the equilateral triangle is 330cm.

    ### Answer: 330

Expected answer: 330

Correct? Yes

🔗 Problem

Problem: A triangle has a perimeter of 997m. Two of its sides have lengths of 2m and 667m. What is the length of the third side?

Gemma 2B:

    Let's use the formula for the perimeter of a triangle:

    Perimeter = a + b + c

    where a, b, and c are the lengths of the three sides.

    We know the perimeter is 997m, and we know two of the sides have lengths 2m and 667m. So, we can set up the equation:

    997 = 2 + 667 + c

    Subtract 2 and 667 from both sides:

    997 - 2 - 667 = c

    c = 328

    So, the length of the third side is 328m.

    ### Answer: 328m

Expected answer: 328

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 579 cm. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 579 cm, so we can set up the equation:

    3x = 579

    To solve for x, we can divide both sides of the equation by 3:

    x = 579 ÷ 3
    x = 193

    So, the length of each side of the equilateral triangle is 193 cm.

    ### Answer: 193

Expected answer: 193

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 684m. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 684m, so we can set up the equation:

    3x = 684

    To solve for x, we can divide both sides of the equation by 3:

    x = 684 ÷ 3
    x = 228

    So, the length of each side of the equilateral triangle is 228m.

    ### Answer: 228

Expected answer: 228

Correct? Yes

🔗 Problem

Problem: A triangle has a perimeter of 503 meters. One side of the triangle is 223 meters long and another side is 46 meters long. What is the length of the remaining side?

Gemma 2B:

    Let's use the formula for the perimeter of a triangle:

    Perimeter = a + b + c

    where a, b, and c are the lengths of the three sides.

    We know the perimeter is 503 meters, and we know two of the sides are 223 meters and 46 meters long. We can set up an equation:

    223 + 46 + c = 503

    Combine like terms:

    269 + c = 503

    Subtract 269 from both sides:

    c = 234

    So, the length of the remaining side is 234 meters.

    ### Answer: 234

Expected answer: 234

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 105m. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Since it's an equilateral triangle, all sides are equal. Let's call the length of each side "x". The perimeter is the sum of all sides, so we can set up the equation:

    x + x + x = 105

    Combine like terms:

    3x = 105

    Divide both sides by 3:

    x = 35

    So, the length of each side is 35m.

    ### Answer: 35m

Expected answer: 35

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 306cm. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 306cm, so we can set up the equation:

    3x = 306

    To solve for x, we can divide both sides of the equation by 3:

    x = 306 ÷ 3
    x = 102

    So, the length of each side of the equilateral triangle is 102cm.

    ### Answer: 102

Expected answer: 102

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 33 cm. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Since it's an equilateral triangle, all three sides are equal. Let's call the length of each side "x". The perimeter is the sum of all three sides, so we can set up the equation:

    x + x + x = 33

    Combine like terms:

    3x = 33

    Divide both sides by 3:

    x = 11

    So, the length of each side is 11 cm.

    ### Answer: 11

Expected answer: 11

Correct? Yes

🔗 Problem

Problem: A triangle has a perimeter of 861m. Two of the sides are known to be 192m and 159m in length. Can you find the length of the third side?

Gemma 2B:

    Let's use the formula for the perimeter of a triangle:

    Perimeter = a + b + c

    where a, b, and c are the lengths of the three sides.

    We know the perimeter is 861m, and we know two of the sides are 192m and 159m. We can set up an equation:

    192 + 159 + c = 861

    Combine like terms:

    351 + c = 861

    Subtract 351 from both sides:

    c = 510

    So, the length of the third side is 510m.

    ### Answer: 510m

Expected answer: 510

Correct? Yes

🔗 Problem

Problem: A triangle has a perimeter of 489 centimeters. If each of its sides is of equal length, what is the length of one side?

Gemma 2B:

    Reasoning: Let's call the length of one side "x". Since the perimeter is the sum of all sides, we can set up the equation:

    x + x + x = 489

    Combine like terms:

    3x = 489

    Divide both sides by 3:

    x = 489/3

    x = 163

    ### Answer: 163

Expected answer: 163

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 696 meters. What is the length of each side of this triangle?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all sides are equal. The perimeter of the triangle is the sum of all its sides, which is 3x. We are given that the perimeter is 696 meters, so we can set up the equation:

    3x = 696

    To solve for x, we can divide both sides of the equation by 3:

    x = 696 ÷ 3
    x = 232

    So, the length of each side of the equilateral triangle is 232 meters.

    ### Answer: 232

Expected answer: 232

Correct? Yes

🔗 Problem

Problem: The perimeter of a triangle is 804m. One side of the triangle is 180m long, and another side is 579m long. What is the length of the third side?

Gemma 2B:

    Reasoning: Let's call the length of the third side "x". The perimeter of a triangle is the sum of the lengths of all its sides, so we can set up the equation:

    180 + 579 + x = 804

    To solve for x, we can subtract 180 and 579 from both sides of the equation:

    x = 804 - 180 - 579

    x = 45

    ### Answer: 45

Expected answer: 45

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 915cm. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 915cm, so we can set up the equation:

    3x = 915

    To solve for x, we can divide both sides of the equation by 3:

    x = 915 ÷ 3
    x = 305

    So, the length of each side of the equilateral triangle is 305cm.

    ### Answer: 305cm

Expected answer: 305

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 564 cm. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 564 cm, so we can set up the equation:

    3x = 564

    To solve for x, we can divide both sides of the equation by 3:

    x = 564 ÷ 3
    x = 188

    So, the length of each side of the equilateral triangle is 188 cm.

    ### Answer: 188

Expected answer: 188

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 594 cm. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 594 cm, so we can set up the equation:

    3x = 594

    To solve for x, we can divide both sides of the equation by 3:

    x = 594 ÷ 3
    x = 198

    So, the length of each side of the equilateral triangle is 198 cm.

    ### Answer: 198

Expected answer: 198

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 453 cm. How long is each side of the triangle?

Gemma 2B:

    Reasoning: Let's call the length of each side of the triangle "x". Since it's an equilateral triangle, all sides are equal. The perimeter is the sum of all sides, which is 3x. We know the perimeter is 453 cm, so we can set up the equation:

    3x = 453

    To solve for x, we can divide both sides by 3:

    x = 453 ÷ 3
    x = 151

    So, each side of the triangle is 151 cm long.

    ### Answer: 151

Expected answer: 151

Correct? Yes

🔗 Problem

Problem: A triangle has a total perimeter of 898m. The lengths of two of its sides are 250m and 435m respectively. Can you find the length of the third side of the triangle?

Gemma 2B:

    Let's use the formula for the perimeter of a triangle:

    Perimeter = a + b + c

    where a, b, and c are the lengths of the three sides.

    We know the total perimeter is 898m, and we know the lengths of two of the sides (250m and 435m). We can set up an equation:

    250 + 435 + c = 898

    Combine like terms:

    685 + c = 898

    Subtract 685 from both sides:

    c = 213

    So, the length of the third side of the triangle is 213m.

    ### Answer: 213m

Expected answer: 213

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a total perimeter of 405 cm. Can you determine the length of each side?

Gemma 2B:

    Reasoning: Since it's an equilateral triangle, all three sides are equal. Let's call the length of each side "x". The perimeter is the sum of all three sides, so we can set up the equation:

    3x = 405

    To find the length of each side, we can divide both sides by 3:

    x = 405 ÷ 3
    x = 135

    So, the length of each side of the equilateral triangle is 135 cm.

    ### Answer: 135 cm

Expected answer: 135

Correct? Yes

🔗 Problem

Problem: Somehow you got lost in the forest and got trapped in a mysterious place where you find an equilateral triangle-shaped space. The total perimeter of this space is 612 meters. Can you find out the length of each side of this triangle?

Gemma 2B:

    Reasoning: Since the space is an equilateral triangle, all three sides are equal. Let's call the length of each side "x". The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We know that the perimeter is 612 meters, so we can set up the equation:

    3x = 612

    To solve for x, we can divide both sides of the equation by 3:

    x = 612 ÷ 3
    x = 204

    So, the length of each side of the equilateral triangle is 204 meters.

    ### Answer: 204

Expected answer: 204

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 591 cm. Can you find the length of each side of this triangle?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides are equal. The perimeter of the triangle is the sum of all three sides, which is 591 cm. We can set up an equation:

    x + x + x = 591

    Combine like terms:

    3x = 591

    Divide both sides by 3:

    x = 197

    So, the length of each side of the equilateral triangle is 197 cm.

    ### Answer: 197

Expected answer: 197

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 858m. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 858m, so we can set up the equation:

    3x = 858

    To solve for x, we can divide both sides of the equation by 3:

    x = 858 ÷ 3
    x = 286

    So, the length of each side of the equilateral triangle is 286m.

    ### Answer: 286m

Expected answer: 286

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 543 meters. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 543 meters, so we can set up the equation:

    3x = 543

    To solve for x, we can divide both sides of the equation by 3:

    x = 543 ÷ 3
    x = 181

    So, the length of each side of the equilateral triangle is 181 meters.

    ### Answer: 181

Expected answer: 181

Correct? Yes

🔗 Problem

Problem: A triangle has three equal sides. If the perimeter of the triangle is 255 meters, what is the length of each side?

Gemma 2B:

    Reasoning: Since the triangle has three equal sides, we can let the length of each side be x.
    The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.
    We are given that the perimeter is 255 meters, so we can set up the equation 3x = 255.
    To solve for x, we can divide both sides of the equation by 3, which gives us x = 255/3.
    x = 85.
    ### Answer: 85

Expected answer: 85

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 570mm. Find the length of each side of this triangle.

Gemma 2B:

    Reasoning: Since the triangle is equilateral, all three sides are equal. Let's call the length of each side "x". The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 570mm, so we can set up the equation:

    3x = 570

    To solve for x, we can divide both sides of the equation by 3:

    x = 570 ÷ 3
    x = 190

    So, the length of each side of the equilateral triangle is 190mm.

    ### Answer: 190mm

Expected answer: 190

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 129m. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Since it's an equilateral triangle, all sides are equal. Let's call the length of each side "x". The perimeter is the sum of all sides, so we can set up the equation:

    x + x + x = 129

    Combine like terms:

    3x = 129

    Divide both sides by 3:

    x = 129/3

    x = 43

    So, the length of each side is 43m.

    ### Answer: 43m

Expected answer: 43

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 858 meters. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 858 meters, so we can set up the equation:

    3x = 858

    To solve for x, we can divide both sides of the equation by 3:

    x = 858 ÷ 3
    x = 286

    So, the length of each side of the equilateral triangle is 286 meters.

    ### Answer: 286

Expected answer: 286

Correct? Yes

🔗 Problem

Problem: A triangle has a perimeter of 513 km, and it's known to be an equilateral triangle - meaning all three sides are of equal length. Can you determine how long each side of this triangle is?

Gemma 2B:

    Reasoning: Since the triangle is equilateral, all three sides are equal. Let's call the length of each side "x". The perimeter of the triangle is the sum of the lengths of all three sides, which is 513 km. We can set up an equation:

    x + x + x = 513

    Combine like terms:

    3x = 513

    Divide both sides by 3:

    x = 171

    So, each side of the triangle is 171 km long.

    ### Answer: 171 km

Expected answer: 171

Correct? Yes

🔗 Problem

Problem: A triangular field has a perimeter of 828 meters. Two sides of the field are 105 and 434 meters long. How long is the third side of the field?

Gemma 2B:

    Let's use the formula for the perimeter of a triangle:

    Perimeter = a + b + c

    where a, b, and c are the lengths of the three sides.

    We know the perimeter is 828 meters, and we know two of the sides are 105 and 434 meters long. We can set up an equation:

    105 + 434 + c = 828

    Combine like terms:

    539 + c = 828

    Subtract 539 from both sides:

    c = 828 - 539

    c = 289

    So, the third side of the field is 289 meters long.

    ### Answer: 289

Expected answer: 289

Correct? Yes

🔗 Problem

Problem: The perimeter of a triangle is 773 cm. Two of its sides measure 37 cm and 559 cm, respectively. Find the length of the third side?

Gemma 2B:

    Reasoning: The perimeter of a triangle is the sum of the lengths of all its sides. Let's denote the length of the third side as x. We can set up the equation:

    37 + 559 + x = 773

    Simplifying the equation, we get:

    596 + x = 773

    Subtracting 596 from both sides, we get:

    x = 177

    ### Answer: 177

Expected answer: 177

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 714m. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 714m, so we can set up the equation:

    3x = 714

    To solve for x, we can divide both sides of the equation by 3:

    x = 714 ÷ 3
    x = 238

    So, the length of each side of the equilateral triangle is 238m.

    ### Answer: 238m

Expected answer: 238

Correct? Yes

🔗 Problem

Problem: In a large triangular garden, one of its sides is 147m and another side is 590m. If the perimeter of the garden is 792m, can you find the length of the third side?

Gemma 2B:

    Reasoning: Let's call the length of the third side "x". Since it's a triangle, the perimeter is the sum of all three sides, which is 792m. We can set up an equation:

    147 + 590 + x = 792

    Combine like terms:

    737 + x = 792

    Subtract 737 from both sides:

    x = 55

    ### Answer: 55

Expected answer: 55

Correct? Yes

🔗 Problem

Problem: The perimeter of a triangle is 871 meters. One of the sides is 321 meters long and another is 528 meters long. What is the length of the third side?

Gemma 2B:

    Reasoning: Let's call the length of the third side "x". The perimeter of a triangle is the sum of the lengths of all its sides, so we can set up the equation:

    321 + 528 + x = 871

    To solve for x, we can subtract 321 and 528 from both sides of the equation:

    x = 871 - 321 - 528

    x = 22

    ### Answer: 22

Expected answer: 22

Correct? Yes

🔗 Problem

Problem: A triangle has a perimeter of 991m. Two sides of the triangle measure 424m and 246m respectively. Find the length of the third side of the triangle.

Gemma 2B:

    Let's use the formula for the perimeter of a triangle:

    Perimeter = a + b + c

    where a, b, and c are the lengths of the three sides.

    We are given that the perimeter is 991m, and two of the sides are 424m and 246m. We can set up an equation:

    424 + 246 + c = 991

    Combine like terms:

    670 + c = 991

    Subtract 670 from both sides:

    c = 991 - 670

    c = 321

    So, the length of the third side of the triangle is 321m.

    ### Answer: 321m.

Expected answer: 321

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 936m. How long is each side of the triangle?

Gemma 2B:

    Reasoning: Let's call the length of each side of the triangle "x". Since it's an equilateral triangle, all sides are equal. The perimeter is the sum of all sides, which is 3x. We know the perimeter is 936m, so we can set up the equation:

    3x = 936

    To solve for x, we can divide both sides by 3:

    x = 936 ÷ 3
    x = 312

    So, each side of the triangle is 312m long.

    ### Answer: 312

Expected answer: 312

Correct? Yes

🔗 Problem

Problem: A triangle has a perimeter of 721m. Two of its sides have lengths of 204m and 195m, respectively. What is the length of the third side of the triangle?

Gemma 2B:

    Reasoning: Let the length of the third side be x. The perimeter of the triangle is the sum of the lengths of all three sides, which is given as 721m. We can set up an equation using the given information:

    204 + 195 + x = 721

    Simplifying the equation, we get:

    399 + x = 721

    Subtracting 399 from both sides gives:

    x = 722 - 399

    x = 323

    ### Answer: 323m

Expected answer: 322

Correct? No

🔗 Problem

Problem: An equilateral triangle has a perimeter of 201m. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 201m, so we can set up the equation:

    3x = 201

    To solve for x, we can divide both sides of the equation by 3:

    x = 201/3

    x = 67

    So, the length of each side of the equilateral triangle is 67m.

    ### Answer: 67

Expected answer: 67

Correct? Yes

🔗 Problem

Problem: A large equilateral triangle has a perimeter of 756m. Find the length of each of its sides.

Gemma 2B:

    Reasoning: Since it's an equilateral triangle, all three sides are equal. Let's call the length of each side "x". The perimeter is the sum of all three sides, so we can set up the equation:

    3x = 756

    To find the length of each side, we can divide both sides of the equation by 3:

    x = 756 ÷ 3
    x = 252

    So, the length of each side of the equilateral triangle is 252m.

    ### Answer: 252

Expected answer: 252

Correct? Yes

🔗 Problem

Problem: The perimeter of a triangle is 923m. Two of its sides are 735m and 144m long respectively. What is the length of the third side?

Gemma 2B:

    Reasoning: Let the length of the third side be x. The perimeter of a triangle is the sum of the lengths of all its sides. So, we can set up the equation:

    735 + 144 + x = 923

    Subtracting 735 and 144 from both sides gives:

    x = 44

    ### Answer: 44

Expected answer: 44

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 813 cm. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 813 cm, so we can set up the equation:

    3x = 813

    To solve for x, we can divide both sides of the equation by 3:

    x = 813 ÷ 3
    x = 271

    So, the length of each side of the equilateral triangle is 271 cm.

    ### Answer: 271 cm.

Expected answer: 271

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 834 feet. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 834 feet, so we can set up the equation:

    3x = 834

    To solve for x, we can divide both sides of the equation by 3:

    x = 834 ÷ 3
    x = 278

    So, the length of each side of the equilateral triangle is 278 feet.

    ### Answer: 278

Expected answer: 278

Correct? Yes

🔗 Problem

Problem: A triangle has a perimeter of 105m and all its sides are equal in length. How long is one side of the triangle?

Gemma 2B:

    Reasoning: Since the perimeter of the triangle is 105m, and all sides are equal, we can divide the perimeter by 3 to find the length of one side.

    105m ÷ 3 = 35m

    ### Answer: 35m

Expected answer: 35

Correct? Yes

🔗 Problem

Problem: A triangle has a perimeter of 195cm. Given that all sides of the triangle are equal, what is the length of each side?

Gemma 2B:

    Reasoning: Since the perimeter of the triangle is 195cm, and all sides are equal, we can divide the perimeter by 3 to find the length of each side.

    Perimeter = 195cm
    Length of each side = Perimeter ÷ 3
    = 195cm ÷ 3
    = 65cm

    ### Answer: 65cm

Expected answer: 65

Correct? Yes

🔗 Problem

Problem: A triangle has a perimeter of 919m. You know that one of its sides is 350m long and the other side is 154m long. What is the length of the third side?

Gemma 2B:

    Reasoning: Let's call the length of the third side "x". Since the perimeter is the sum of all three sides, we can set up the equation:

    350 + 154 + x = 919

    Combine like terms:

    504 + x = 919

    Subtract 504 from both sides:

    x = 415

    ### Answer: 415

Expected answer: 415

Correct? Yes

🔗 Problem

Problem: A triangle has a perimeter of 989m. You know that two of its sides are 128m and 288m long respectively. What is the length of the third side?

Gemma 2B:

    Let's use the formula for the perimeter of a triangle:

    Perimeter = a + b + c

    where a, b, and c are the lengths of the three sides.

    We know the perimeter is 989m, and we know two of the sides are 128m and 288m long. So, we can set up the equation:

    128 + 288 + c = 989

    Combine like terms:

    416 + c = 989

    Subtract 416 from both sides:

    c = 989 - 416

    c = 573

    So, the length of the third side is 573m.

    ### Answer: 573m.

Expected answer: 573

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 321 meters. If all sides are equal, what is the length of each side of the triangle?

Gemma 2B:

    Reasoning: Let's call the length of each side of the triangle "x". Since it's an equilateral triangle, all sides are equal, so the perimeter is 3x.
    We know the perimeter is 321 meters, so we can set up the equation: 3x = 321.
    To solve for x, we can divide both sides by 3: x = 321/3.
    x = 107.
    ### Answer: 107

Expected answer: 107

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 258 cm. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 258 cm, so we can set up the equation:

    3x = 258

    To solve for x, we can divide both sides of the equation by 3:

    x = 258 ÷ 3
    x = 86

    So, the length of each side of the equilateral triangle is 86 cm.

    ### Answer: 86 cm.

Expected answer: 86

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 75m. What is the length of each side of the triangle?

Gemma 2B:

    Reasoning: Since the triangle is equilateral, all three sides are equal. Let's call the length of each side "x". The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 75m, so we can set up the equation:

    3x = 75

    To solve for x, we can divide both sides by 3:

    x = 75/3

    x = 25

    So, the length of each side of the triangle is 25m.

    ### Answer: 25m

Expected answer: 25

Correct? Yes

🔗 Problem

Problem: The perimeter of a triangle is 979m. Two of its sides are 620m and 80m respectively. What is the length of the third side?

Gemma 2B:

    Reasoning: Let the length of the third side be x. The perimeter of a triangle is the sum of the lengths of all its sides. Therefore, we can set up the equation:

    620 + 80 + x = 979

    Simplifying the equation, we get:

    700 + x = 979

    Subtracting 700 from both sides, we get:

    x = 979 - 700

    x = 279

    ### Answer: 279

Expected answer: 279

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 966 meters. What is the length of each side of this triangle?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all sides are equal. The perimeter of the triangle is the sum of all its sides, which is 3x. We are given that the perimeter is 966 meters, so we can set up the equation:

    3x = 966

    To solve for x, we can divide both sides of the equation by 3:

    x = 966 ÷ 3
    x = 322

    So, the length of each side of the equilateral triangle is 322 meters.

    ### Answer: 322

Expected answer: 322

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 486 cm. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 486 cm, so we can set up the equation:

    3x = 486

    To solve for x, we can divide both sides of the equation by 3:

    x = 486 ÷ 3
    x = 162

    So, the length of each side of the equilateral triangle is 162 cm.

    ### Answer: 162 cm.

Expected answer: 162

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 948 meters. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 948 meters, so we can set up the equation:

    3x = 948

    To solve for x, we can divide both sides of the equation by 3:

    x = 948 ÷ 3
    x = 316

    So, the length of each side of the equilateral triangle is 316 meters.

    ### Answer: 316

Expected answer: 316

Correct? Yes

🔗 Problem

Problem: A scalene triangle has three sides of different lengths. The first side is 252m, and the second side is 687m. The total perimeter of the triangle is 998m. Can you find the length of the third side?

Gemma 2B:

    Let's call the length of the third side "x". Since it's a scalene triangle, the three sides have different lengths, so we can't use any of the special triangle formulas that rely on equal sides.

    Instead, we can use the fact that the perimeter of the triangle is the sum of the lengths of all three sides. We know the perimeter is 998m, and we know two of the sides are 252m and 687m. So, we can set up the equation:

    252 + 687 + x = 998

    To solve for x, we can subtract 252 and 687 from both sides of the equation:

    x = 998 - 252 - 687
    x = 59

    So, the length of the third side is 59m.

    ### Answer: 59m.

Expected answer: 59

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 618m. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 618m, so we can set up the equation:

    3x = 618

    To solve for x, we can divide both sides of the equation by 3:

    x = 618 ÷ 3
    x = 206

    So, the length of each side of the equilateral triangle is 206m.

    ### Answer: 206m

Expected answer: 206

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 483 meters. How long is each side?

Gemma 2B:

    Reasoning: Let's call the length of each side "x". Since it's an equilateral triangle, all sides are equal. The perimeter is the sum of all sides, which is 3x. We know the perimeter is 483 meters, so we can set up the equation:

    3x = 483

    To solve for x, we can divide both sides by 3:

    x = 483 ÷ 3
    x = 161

    So, each side of the equilateral triangle is 161 meters long.

    ### Answer: 161

Expected answer: 161

Correct? Yes

🔗 Problem

Problem: A triangle has a perimeter of 804m. One of its sides is 262m long and another is 90m long. What is the length of the third side?

Gemma 2B:

    Let's use the formula for the perimeter of a triangle:

    Perimeter = a + b + c

    where a, b, and c are the lengths of the three sides.

    We know the perimeter is 804m, and we know two of the sides are 262m and 90m. We can plug these values into the formula:

    804 = 262 + 90 + c

    First, let's add 262 and 90:

    804 = 352 + c

    Now, subtract 352 from both sides:

    804 - 352 = c

    452 = c

    So, the length of the third side is 452m.

    ### Answer: 452

Expected answer: 452

Correct? Yes

🔗 Problem

Problem: A large triangle has a perimeter of 925m. Two of its sides are 183m and 498m, respectively. What is the length of the third side?

Gemma 2B:

    Reasoning: Let's call the length of the third side "x". We can use the formula for the perimeter of a triangle to set up an equation:

    183 + 498 + x = 925

    Combine like terms:

    681 + x = 925

    Subtract 681 from both sides:

    x = 244

    ### Answer: 244

Expected answer: 244

Correct? Yes

🔗 Problem

Problem: A scalene triangle has a total perimeter of 573m. One of its sides measures 103m and another side measures 386m. What is the length of the third side?

Gemma 2B:

    Let's call the length of the third side "x".

    Since it's a scalene triangle, all sides are unequal. We can use the fact that the perimeter is the sum of all sides to set up an equation:

    103 + 386 + x = 573

    Combine like terms:

    489 + x = 573

    Subtract 489 from both sides:

    x = 84

    So, the length of the third side is 84m.

    ### Answer: 84m

Expected answer: 84

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 330m. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Since it's an equilateral triangle, all three sides are equal. Let's call the length of each side "x". The perimeter is the sum of all three sides, so we can set up the equation:

    x + x + x = 330

    Combine like terms:

    3x = 330

    Divide both sides by 3:

    x = 330/3

    x = 110

    So, the length of each side is 110m.

    ### Answer: 110

Expected answer: 110

Correct? Yes

🔗 Problem

Problem: A triangle has a perimeter of 850m. Two of its sides have lengths of 57m and 426m, respectively. What is the length of the third side?

Gemma 2B:

    Let's use the formula for the perimeter of a triangle:

    Perimeter = a + b + c

    where a, b, and c are the lengths of the three sides.

    We know the perimeter is 850m, and we know two of the sides have lengths 57m and 426m. So, we can set up the equation:

    850 = 57 + 426 + c

    Now, we can simplify the equation by combining the known side lengths:

    850 = 483 + c

    Subtract 483 from both sides to get:

    367 = c

    So, the length of the third side is 367m.

    ### Answer: 367m.

Expected answer: 367

Correct? Yes

🔗 Problem

Problem: A triangle has a perimeter of 764m. Two of its sides are 265m and 56m in length. What is the length of the third side?

Gemma 2B:

    Let's use the formula for the perimeter of a triangle:

    Perimeter = a + b + c

    where a, b, and c are the lengths of the three sides.

    We know the perimeter is 764m, and we know two of the sides are 265m and 56m. So, we can set up the equation:

    265 + 56 + c = 764

    Combine like terms:

    321 + c = 764

    Subtract 321 from both sides:

    c = 443

    So, the length of the third side is 443m.

    ### Answer: 443

Expected answer: 443

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 723cm. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 723cm, so we can set up the equation:

    3x = 723

    To solve for x, we can divide both sides of the equation by 3:

    x = 723 ÷ 3
    x = 241

    So, the length of each side of the equilateral triangle is 241cm.

    ### Answer: 241cm

Expected answer: 241

Correct? Yes

🔗 Problem

Problem: A triangle has a side with a length of 315m and another side with a length of 100m. If the perimeter of the triangle is 738m, what is the length of the third side?

Gemma 2B:

    Let's use the formula for the perimeter of a triangle:

    Perimeter = a + b + c

    where a and b are the given side lengths, and c is the length of the third side.

    We know the perimeter is 738m, and we know the lengths of two sides:

    a = 315m
    b = 100m
    Perimeter = 738m

    We can set up an equation:

    315 + 100 + c = 738

    Now, let's simplify the equation:

    415 + c = 738

    Subtract 415 from both sides:

    c = 738 - 415

    c = 323

    So, the length of the third side is 323m.

    ### Answer: 323m

Expected answer: 323

Correct? Yes

🔗 Problem

Problem: A triangle has a perimeter of 762m. If one of the sides measures 131m, and the other side is 147m long, what is the length of the third side?

Gemma 2B:

    Reasoning: Let's call the length of the third side "x". Since the perimeter is the sum of all three sides, we can set up the equation:

    131 + 147 + x = 762

    Combine like terms:

    278 + x = 762

    Subtract 278 from both sides:

    x = 484

    ### Answer: 484

Expected answer: 484

Correct? Yes

🔗 Problem

Problem: A triangle has a perimeter of 784m and you know the sum of two of its sides is 472m. What is the length of the third side?

Gemma 2B:

    Let's say the length of the third side is x.

    We know that the sum of two sides is 472m, so we can set up the equation:

    a + b = 472

    We also know that the perimeter is 784m, so we can set up the equation:

    a + b + x = 784

    Subtracting the first equation from the second equation, we get:

    x = 784 - 472
    x = 312

    So, the length of the third side is 312m.

    ### Answer: 312

Expected answer: 312

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 543mm. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 543mm, so we can set up the equation:

    3x = 543

    To solve for x, we can divide both sides of the equation by 3:

    x = 543 ÷ 3
    x = 181

    So, the length of each side of the equilateral triangle is 181mm.

    ### Answer: 181mm

Expected answer: 181

Correct? Yes

🔗 Problem

Problem: A triangle has a first side length of 287m, a second side length of 475m, and a perimeter of 867m. What is the length of the third side?

Gemma 2B:

    Reasoning: Let's denote the length of the third side as x. Since the perimeter is the sum of all three sides, we can set up the equation:

    287 + 475 + x = 867

    Subtracting 287 and 475 from both sides gives:

    x = 867 - 287 - 475
    x = 105

    ### Answer: 105m

Expected answer: 105

Correct? Yes

🔗 Problem

Problem: The perimeter of a triangle is 934m. The lengths of two of its sides add up to 838m (one is 828m and the other is 10m). What is the length of the third side?

Gemma 2B:

    Let's use the information given to find the length of the third side.

    The perimeter of the triangle is 934m, which means the sum of the lengths of all three sides is 934m.

    We know the lengths of two sides: one is 828m and the other is 10m. Let's add these two lengths together:

    828m + 10m = 838m

    This is equal to the sum of the lengths of the two sides mentioned in the problem, which is 838m. Now, we can set up an equation:

    828m + 10m + x = 934m

    where x is the length of the third side.

    Combine like terms:

    838m + x = 934m

    Subtract 838m from both sides:

    x = 934m - 838m

    x = 96m

    So, the length of the third side is 96m.

    ### Answer: 96m.

Expected answer: 96

Correct? Yes

🔗 Problem

Problem: A triangle has a perimeter of 677m. Two of its sides measure 109m and 530m respectively. What is the length of the third side?

Gemma 2B:

    Let's use the formula for the perimeter of a triangle:

    Perimeter = a + b + c

    where a, b, and c are the lengths of the three sides.

    We know the perimeter is 677m, and we know two of the sides are 109m and 530m. So, we can set up the equation:

    677 = 109 + 530 + c

    Now, we can simplify the equation by combining the known sides:

    677 = 639 + c

    Subtract 639 from both sides to get:

    38 = c

    So, the length of the third side is 38m.

    ### Answer: 38

Expected answer: 38

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 582 cm. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 582 cm, so we can set up the equation:

    3x = 582

    To solve for x, we can divide both sides of the equation by 3:

    x = 582 ÷ 3
    x = 194

    So, the length of each side of the equilateral triangle is 194 cm.

    ### Answer: 194

Expected answer: 194

Correct? Yes

🔗 Problem

Problem: A triangle has a perimeter of 499m. Its largest side is 259m long, and one of the other sides is 11m long. What is the length of the last side?

Gemma 2B:

    Let's use the formula for the perimeter of a triangle:

    Perimeter = a + b + c

    where a, b, and c are the lengths of the three sides.

    We know the perimeter is 499m, and we know two of the sides: 259m and 11m. Let's call the length of the third side "x".

    We can set up an equation:

    259 + 11 + x = 499

    Combine like terms:

    270 + x = 499

    Subtract 270 from both sides:

    x = 229

    So, the length of the last side is 229m.

    ### Answer: 229

Expected answer: 229

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 966m. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 966m, so we can set up the equation:

    3x = 966

    To solve for x, we can divide both sides of the equation by 3:

    x = 966 ÷ 3
    x = 322

    So, the length of each side of the equilateral triangle is 322m.

    ### Answer: 322

Expected answer: 322

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 894 inches. What is the length of each side of the triangle?

Gemma 2B:

    Reasoning: Let's call the length of each side of the triangle "x". Since it's an equilateral triangle, all sides are equal. The perimeter is the sum of all sides, which is 3x. We know the perimeter is 894 inches, so we can set up the equation:

    3x = 894

    To solve for x, we can divide both sides by 3:

    x = 894 ÷ 3
    x = 298

    So, the length of each side of the triangle is 298 inches.

    ### Answer: 298

Expected answer: 298

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 891cm. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 891cm, so we can set up the equation:

    3x = 891

    To solve for x, we can divide both sides of the equation by 3:

    x = 891 ÷ 3
    x = 297

    So, the length of each side of the equilateral triangle is 297cm.

    ### Answer: 297cm

Expected answer: 297

Correct? Yes

🔗 Problem

Problem: A triangle has a perimeter of 762 meters. Two sides of these triangle are known to be 122 meters and 245 meters long respectively. Can you calculate the length of the third side?

Gemma 2B:

    Reasoning: Let's call the length of the third side "x". We can use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Since we know the perimeter is 762 meters, we can set up the equation:

    122 + 245 + x = 762

    Subtracting 122 and 245 from both sides gives us:

    x = 395

    So, the length of the third side is 395 meters.

    ### Answer: 395

Expected answer: 395

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 411m. What is the length of each side of the triangle?

Gemma 2B:

    Reasoning: Let's call the length of each side of the triangle "x". Since it's an equilateral triangle, all sides are equal. The perimeter is the sum of all sides, which is 3x. We know the perimeter is 411m, so we can set up the equation:

    3x = 411

    To solve for x, we can divide both sides by 3:

    x = 411/3
    x = 137

    So, the length of each side of the triangle is 137m.

    ### Answer: 137

Expected answer: 137

Correct? Yes

🔗 Problem

Problem: A triangle has three identical sides and the total length of the sides is 72m. What is the length of each side of the triangle?

Gemma 2B:

    Reasoning: Since the triangle has three identical sides, the length of each side is the same. Let's call this length "x".
    The total length of the sides is 72m, so we can set up the equation: 3x = 72
    To find the length of each side, we can divide both sides of the equation by 3: x = 72/3
    x = 24
    ### Answer: 24m

Expected answer: 24

Correct? Yes

🔗 Problem

Problem: A large triangle has a perimeter of 930 meters. Two of its sides measure 537 meters and 68 meters respectively. What is the length of the third side?

Gemma 2B:

    Let's use the formula for the perimeter of a triangle:

    Perimeter = a + b + c

    where a, b, and c are the lengths of the three sides.

    We know the perimeter is 930 meters, and we know two of the sides are 537 meters and 68 meters. We can plug these values into the formula:

    930 = 537 + 68 + c

    First, let's add the known sides:

    930 = 605 + c

    Now, subtract 605 from both sides:

    930 - 605 = c

    c = 325

    So, the length of the third side is 325 meters.

    ### Answer: 325

Expected answer: 325

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 657 meters. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 657 meters, so we can set up the equation:

    3x = 657

    To solve for x, we can divide both sides of the equation by 3:

    x = 657 ÷ 3
    x = 219

    So, the length of each side of the equilateral triangle is 219 meters.

    ### Answer: 219

Expected answer: 219

Correct? Yes

🔗 Problem

Problem: A scalene triangle has a side that measures 368m and another side that measures 230m. If the perimeter of the triangle is 909m, what is the length of the third side?

Gemma 2B:

    Reasoning: Let's call the length of the third side "x". Since it's a scalene triangle, all sides are different. We can set up an equation using the formula for the perimeter of a triangle:

    P = a + b + c

    where P is the perimeter, and a, b, and c are the lengths of the sides. We know the perimeter is 909m, and we know two of the sides are 368m and 230m. So, we can plug in the values:

    909 = 368 + 230 + x

    Simplifying the equation, we get:

    909 = 598 + x

    Subtracting 598 from both sides gives us:

    311 = x

    So, the length of the third side is 311m.

    ### Answer: 311m.

Expected answer: 311

Correct? Yes

🔗 Problem

Problem: A triangle has a perimeter of 700 m. Two of its sides are 140m and 525m long. What is the length of the third side?

Gemma 2B:

    Let's use the formula for the perimeter of a triangle:

    Perimeter = a + b + c

    where a, b, and c are the lengths of the three sides.

    We know the perimeter is 700m, and we know two of the sides are 140m and 525m long. So, we can set up the equation:

    700 = 140 + 525 + c

    Now, we can simplify the equation by combining the constants:

    700 = 665 + c

    Subtract 665 from both sides:

    35 = c

    So, the length of the third side is 35m.

    ### Answer: 35

Expected answer: 35

Correct? Yes

🔗 Problem

Problem: A triangle has a perimeter of 915cm. Two of its sides are 484cm and 130cm respectively. What length is the third side of the triangle?

Gemma 2B:

    Let's use the formula for the perimeter of a triangle:

    Perimeter = a + b + c

    where a, b, and c are the lengths of the three sides.

    We know the perimeter is 915cm, and we know two of the sides are 484cm and 130cm. So, we can set up the equation:

    915 = 484 + 130 + c

    Now, we can solve for c:

    915 = 614 + c

    Subtract 614 from both sides:

    301 = c

    So, the length of the third side of the triangle is 301cm.

    ### Answer: 301cm.

Expected answer: 301

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 120 cm. How long is each side of the triangle?

Gemma 2B:

    Reasoning: Let's call the length of each side of the triangle "x". Since it's an equilateral triangle, all sides are equal. The perimeter is the sum of all sides, which is 120 cm. We can set up an equation:

    x + x + x = 120

    Combine like terms:

    3x = 120

    Divide both sides by 3:

    x = 40

    So, each side of the triangle is 40 cm long.

    ### Answer: 40 cm

Expected answer: 40

Correct? Yes

🔗 Problem

Problem: A triangular field has a perimeter of 661m. Two sides of the field are known to be 382m and 151m respectively. What is the length of the third side?

Gemma 2B:

    Let's use the formula for the perimeter of a triangle:

    Perimeter = a + b + c

    where a, b, and c are the lengths of the three sides.

    We know the perimeter is 661m, and we know two of the sides are 382m and 151m. We can set up an equation:

    382 + 151 + c = 661

    Combine like terms:

    533 + c = 661

    Subtract 533 from both sides:

    c = 128

    So, the length of the third side is 128m.

    ### Answer: 128

Expected answer: 128

Correct? Yes

🔗 Problem

Problem: A triangle has a total perimeter of 678 feet. Two of its sides measure 419 feet and 164 feet respectively. What is the length of the third side?

Gemma 2B:

    Let's use the formula for the perimeter of a triangle:

    Perimeter = a + b + c

    where a, b, and c are the lengths of the three sides.

    We know the total perimeter is 678 feet, and we know the lengths of two of the sides: 419 feet and 164 feet. We can set up an equation:

    419 + 164 + c = 678

    To solve for c, we can subtract 419 and 164 from both sides:

    c = 678 - 419 - 164
    c = 95

    So, the length of the third side is 95 feet.

    ### Answer: 95

Expected answer: 95

Correct? Yes

🔗 Problem

Problem: The perimeter of a triangle is 248m. Two of the sides are 186m and 37m long, respectively. What is the length of the remaining side?

Gemma 2B:

    Reasoning: The perimeter of a triangle is the sum of the lengths of all its sides. Let's denote the length of the remaining side as x. We can set up the equation:

    186 + 37 + x = 248

    To solve for x, we can subtract 186 and 37 from both sides:

    x = 248 - 186 - 37
    x = 25

    ### Answer: 25

Expected answer: 25

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 246 centimeters. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 246 centimeters, so we can set up the equation:

    3x = 246

    To solve for x, we can divide both sides of the equation by 3:

    x = 246 ÷ 3
    x = 82

    So, the length of each side of the equilateral triangle is 82 centimeters.

    ### Answer: 82

Expected answer: 82

Correct? Yes

🔗 Problem

Problem: The total perimeter of a triangular field is 739 meters. Two of its sides measure 180 meters and 338 meters respectively. Find the length of the third side.

Gemma 2B:

    Let's use the formula for the perimeter of a triangle:

    Perimeter = a + b + c

    where a, b, and c are the lengths of the three sides.

    We know the total perimeter is 739 meters, and we know two of the sides are 180 meters and 338 meters. We can set up an equation:

    180 + 338 + c = 739

    Combine like terms:

    518 + c = 739

    Subtract 518 from both sides:

    c = 221

    So, the length of the third side is 221 meters.

    ### Answer: 221

Expected answer: 221

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 684cm. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Since it's an equilateral triangle, all three sides are equal. Let's call the length of each side "x". The perimeter is the sum of all three sides, so we can set up the equation:

    3x = 684

    To find the length of each side, we can divide both sides by 3:

    x = 684 ÷ 3
    x = 228

    ### Answer: 228cm

Expected answer: 228

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 537m. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 537m, so we can set up the equation:

    3x = 537

    To solve for x, we can divide both sides of the equation by 3:

    x = 537 ÷ 3
    x = 179

    So, the length of each side of the equilateral triangle is 179m.

    ### Answer: 179

Expected answer: 179

Correct? Yes

🔗 Problem

Problem: A triangle has a perimeter of 568m. The lengths of two of its sides are 110m and 205m. What is the length of the third side?

Gemma 2B:

    Let's use the formula for the perimeter of a triangle:

    Perimeter = a + b + c

    where a, b, and c are the lengths of the three sides.

    We know the perimeter is 568m, and we know the lengths of two of the sides: 110m and 205m. We can set up an equation:

    110 + 205 + c = 568

    Combine like terms:

    315 + c = 568

    Subtract 315 from both sides:

    c = 253

    So, the length of the third side is 253m.

    ### Answer: 253m

Expected answer: 253

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 942mm. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 942mm, so we can set up the equation:

    3x = 942

    To solve for x, we can divide both sides of the equation by 3:

    x = 942 ÷ 3
    x = 314

    So, the length of each side of the equilateral triangle is 314mm.

    ### Answer: 314mm

Expected answer: 314

Correct? Yes

🔗 Problem

Problem: A triangular garden has one side that is 325 meters long and another that is 15 meters long. The total perimeter of the triangle is 633 meters. What is the length of the third side of the garden?

Gemma 2B:

    Reasoning: Let's call the length of the third side "x". The perimeter of the triangle is the sum of all its sides, which is 633 meters. We know that one side is 325 meters and another is 15 meters, so we can set up the equation:

    325 + 15 + x = 633

    Simplifying the equation, we get:

    340 + x = 633

    Subtracting 340 from both sides gives us:

    x = 293

    ### Answer: 293

Expected answer: 293

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 504 meters. What is the length of each side of the triangle?

Gemma 2B:

    Reasoning: Let's call the length of each side of the triangle "x". Since it's an equilateral triangle, all sides are equal. The perimeter is the sum of all sides, which is 3x. We know the perimeter is 504 meters, so we can set up the equation:

    3x = 504

    To solve for x, we can divide both sides by 3:

    x = 504 / 3
    x = 168

    So, the length of each side of the triangle is 168 meters.

    ### Answer: 168

Expected answer: 168

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 51 cm. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Since it's an equilateral triangle, all sides are equal. Let's call the length of each side "x". The perimeter is the sum of all sides, so we can set up the equation:

    x + x + x = 51

    Combine like terms:

    3x = 51

    Divide both sides by 3:

    x = 17

    So, the length of each side is 17 cm.

    ### Answer: 17 cm.

Expected answer: 17

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 501 feet. What is the length of each side of the triangle?

Gemma 2B:

    Reasoning: Let's call the length of each side of the triangle "x". Since it's an equilateral triangle, all sides are equal. The perimeter is the sum of all sides, which is 3x. We know the perimeter is 501 feet, so we can set up the equation:

    3x = 501

    To solve for x, we can divide both sides by 3:

    x = 501/3

    x = 167

    So, the length of each side of the triangle is 167 feet.

    ### Answer: 167

Expected answer: 167

Correct? Yes

🔗 Problem

Problem: The perimeter of an equilateral triangle is 411 meters. What is the length of each side of the triangle?

Gemma 2B:

    Reasoning: The perimeter of an equilateral triangle is the sum of the lengths of all its sides. Since it is an equilateral triangle, all its sides are equal. Let's call the length of each side "x". Then, the perimeter is 3x.

    We know that the perimeter is 411 meters, so we can set up the equation:

    3x = 411

    To solve for x, we can divide both sides by 3:

    x = 411 / 3

    x = 137

    So, the length of each side of the triangle is 137 meters.

    ### Answer: 137

Expected answer: 137

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 114cm. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Since it's an equilateral triangle, all three sides are equal. Let's call the length of each side "x". The perimeter is the sum of all three sides, so we can set up the equation:

    x + x + x = 114

    Combine like terms:

    3x = 114

    Divide both sides by 3:

    x = 38

    So, the length of each side is 38cm.

    ### Answer: 38cm

Expected answer: 38

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 69m. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Since it's an equilateral triangle, all three sides are equal. Let's call the length of each side "x". The perimeter is the sum of all three sides, so we can set up the equation:

    x + x + x = 69

    Combine like terms:

    3x = 69

    Divide both sides by 3:

    x = 69/3

    x = 23

    So, the length of each side is 23m.

    ### Answer: 23m

Expected answer: 23

Correct? Yes

🔗 Problem

Problem: A triangle has sides of lengths 464m and 377m respectively. If the total perimeter of the triangle is 907m, what is the length of the third side?

Gemma 2B:

    Let's denote the length of the third side as x.

    We know that the total perimeter of the triangle is 907m, which is the sum of the lengths of all three sides. Therefore, we can set up the equation:

    464 + 377 + x = 907

    Combine like terms:

    841 + x = 907

    Subtract 841 from both sides:

    x = 907 - 841

    x = 66

    So, the length of the third side is 66m.

    ### Answer: 66m.

Expected answer: 66

Correct? Yes

🔗 Problem

Problem: An equilateral triangle has a perimeter of 966m. What is the length of each of its sides?

Gemma 2B:

    Reasoning: Let's call the length of each side of the equilateral triangle "x". Since it's an equilateral triangle, all three sides have the same length. The perimeter of the triangle is the sum of the lengths of all three sides, which is 3x.

    We are given that the perimeter is 966m, so we can set up the equation:

    3x = 966

    To solve for x, we can divide both sides of the equation by 3:

    x = 966 ÷ 3
    x = 322

    So, the length of each side of the equilateral triangle is 322m.

    ### Answer: 322m

Expected answer: 322

Correct? Yes