Common Core Standard 3.MD.D.8-triangle
This standard covers the following:
Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
Problem: An equilateral triangle has a perimeter of 990cm. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 990 = 3s. 3s = 990. s = 330. ### Answer: 330 **Note:** This is just an example, you can write your own problem and solution below.
Expected answer: 330
Correct? Yes
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 7B:
Reasoning: The perimeter is the sum of the lengths of the three sides. 2m + 667m = 669m. Therefore, the length of the third side is 669m - 2m - 667m = 3m. ### Answer: 3m
Expected answer: 328
Correct? No
Problem: An equilateral triangle has a perimeter of 579 cm. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 579 = 3s. 3s = 579. s = 190. ### Answer: 190 **Note:** This is just an example of how I will solve the problem. The actual problem and answer may vary.
Expected answer: 193
Correct? No
Problem: An equilateral triangle has a perimeter of 684m. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 684/3 = <<684/3=228>>228m is the length of each side. ### Answer: 228
Expected answer: 228
Correct? Yes
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 7B:
Reasoning: The perimeter is the sum of the lengths of the three sides of a triangle. Therefore, the length of the remaining side is 503 - 223 - 46 = 234 meters. ### Answer: 234
Expected answer: 234
Correct? Yes
Problem: An equilateral triangle has a perimeter of 105m. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 105 = 3s. 3s = 105. s = 35m. ### Answer: 35m
Expected answer: 35
Correct? Yes
Problem: An equilateral triangle has a perimeter of 306cm. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 306 = 3s. 3s = 306. s = 102. ### Answer: 102 **Note:** This is just an example of how I will solve the problem. You can replace "Natalia sold clips to 48 of her friends in April, and then she sold half as many clips in May" with your own problem.
Expected answer: 102
Correct? Yes
Problem: An equilateral triangle has a perimeter of 33 cm. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 33 = 3s. 3s = 33, so s = 11. ### Answer: 11
Expected answer: 11
Correct? Yes
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 7B:
Reasoning: The perimeter is the sum of the length of the three sides. Therefore, 861 = 192 + 159 + x. 861 - 192 - 159 = x. 510 = x. x = 510. ### Answer: 510 **Note:** This is just an example of how I would solve the problem. You can use your own method to solve the problem, but you must include your reasoning in the process.
Expected answer: 510
Correct? Yes
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 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. Therefore, the length of one side is 489/3 = <<489/3=163>>163 centimeters. ### Answer: 163
Expected answer: 163
Correct? Yes
Problem: An equilateral triangle has a perimeter of 696 meters. What is the length of each side of this triangle?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, the length of each side of the equilateral triangle is 696/3 = 232 meters. ### Answer: 232
Expected answer: 232
Correct? Yes
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 7B:
Reasoning: The perimeter is the sum of the lengths of the three sides of a triangle. 804 = 180 + 579 + x. Therefore, x = 804 - 180 - 579 = 645m. ### Answer: 645
Expected answer: 45
Correct? No
Problem: An equilateral triangle has a perimeter of 915cm. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 915 = 3s. 3s = 915, so s = 305cm. ### Answer: 305 **Final Answer:** The total number of clips sold by Natalia in April and May is 72. The length of each side of an equilateral triangle with a perimeter of 915cm is 305cm.
Expected answer: 305
Correct? Yes
Problem: An equilateral triangle has a perimeter of 564 cm. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 564/3 = <<564/3=188>>188 cm is the length of each side. ### Answer: 188
Expected answer: 188
Correct? Yes
Problem: An equilateral triangle has a perimeter of 594 cm. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 594 = 3s. 3s = 594, so s = 198. ### Answer: 198
Expected answer: 198
Correct? Yes
Problem: An equilateral triangle has a perimeter of 453 cm. How long is each side of the triangle?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 453 = 3s. 3s = 453. s = 151. ### Answer: 151 **Note:** This is just an example of how I will solve the problem. You can replace "Natalia sold clips to 48 of her friends in April, and then she sold half as many clips in May" with your own problem.
Expected answer: 151
Correct? Yes
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 7B:
Reasoning: The perimeter is the sum of the lengths of the three sides. Therefore, 898 = 250 + 435 + x. x = 898 - 250 - 435 = 213m. ### Answer: 213m
Expected answer: 213
Correct? Yes
Problem: An equilateral triangle has a total perimeter of 405 cm. Can you determine the length of each side?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the length of its sides. Therefore, 405/3 = <<405/3=135>>135 cm is the length of each side. ### Answer: 135 **Note:** You are not required to write the reasoning for the second problem, as it is a simple formula.
Expected answer: 135
Correct? Yes
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 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, the length of each side is 612/3 = <<612/3=204>> meters. ### Answer: 204 **Note:** You are not required to write the reasoning for the second problem, as it is not related to the first problem.
Expected answer: 204
Correct? Yes
Problem: An equilateral triangle has a perimeter of 591 cm. Can you find the length of each side of this triangle?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the length of its sides. Therefore, 591 = 3x + 3x. 3x = 591 - 3x. 6x = 591. x = 591/6. ### Answer: 98 cm **Note:** This is just an example of how I will solve the problem. I will not necessarily solve the problem in the exact same way as you. However, I will always explain my reasoning clearly and format my final answer in the same way.
Expected answer: 197
Correct? No
Problem: An equilateral triangle has a perimeter of 858m. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 858/3 = <<858/3=286>>286m is the length of each side. ### Answer: 286
Expected answer: 286
Correct? Yes
Problem: An equilateral triangle has a perimeter of 543 meters. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 543/3 = <<543/3=181>>181 meters is the length of each side. ### Answer: 181
Expected answer: 181
Correct? Yes
Problem: A triangle has three equal sides. If the perimeter of the triangle is 255 meters, what is the length of each side?
Gemma 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. Therefore, if the perimeter is 255 meters, then each side must be 255/3 = 85 meters long. ### Answer: 85
Expected answer: 85
Correct? Yes
Problem: An equilateral triangle has a perimeter of 570mm. Find the length of each side of this triangle.
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the length of its sides. Therefore, 570 = 3s. 3s = 570. s = 190. ### Answer: 190mm
Expected answer: 190
Correct? Yes
Problem: An equilateral triangle has a perimeter of 129m. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, the length of each side is 129/3 = 43m. ### Answer: 43m
Expected answer: 43
Correct? Yes
Problem: An equilateral triangle has a perimeter of 858 meters. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 858/3 = <<858/3=286>>286 meters is the length of each side. ### Answer: 286
Expected answer: 286
Correct? Yes
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 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the three side lengths. Therefore, each side length is 513/3 = <<513/3=171>>171 km long. ### Answer: 171
Expected answer: 171
Correct? Yes
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 7B:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its sides. Therefore, 828 = 105 + 434 + x. 828 - 105 - 434 = x. 309 = x. x = 309. ### Answer: 309 **Note:** This is just an example of how I would solve the problem. You may not need to include all of the reasoning steps if you are confident in your ability to solve the problem.
Expected answer: 289
Correct? No
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 7B:
Reasoning: The perimeter is the sum of the lengths of the three sides. 37 + 559 = 596 cm. The remaining side is 17 cm. ### Answer: 17 **Note:** This is just an example of how you should format your response. You can use your own unique style and wording, but the final answer should always be formatted as shown above.
Expected answer: 177
Correct? No
Problem: An equilateral triangle has a perimeter of 714m. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 714/3 = <<714/3=238>>238m is the length of each side. ### Answer: 238
Expected answer: 238
Correct? Yes
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 7B:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its sides. Therefore, 792 = 147 + 590 + x. x = 792 - 147 - 590 = 65. ### Answer: 65 **Note:** This is just an example of how I would solve the problem. You can use your own method to solve the problem, but the final answer should be formatted as shown above.
Expected answer: 55
Correct? No
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 7B:
Reasoning: The perimeter is the sum of the lengths of the three sides. 871 = 321 + 528 + x. Therefore, x = 871 - 321 - 528 = 122 meters. ### Answer: 122
Expected answer: 22
Correct? No
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 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Therefore, the length of the third side is 991 - 424 - 246 = 221m. ### Answer: 221 **Final Answer:** The total number of clips sold by Natalia in April and May is 72. The length of the third side of the triangle is 221m.
Expected answer: 321
Correct? No
Problem: An equilateral triangle has a perimeter of 936m. How long is each side of the triangle?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 936 = 3s. 3s = 936. s = 936/3 = 312m. ### Answer: 312m
Expected answer: 312
Correct? Yes
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 7B:
Reasoning: The perimeter is the sum of the lengths of the three sides of a triangle. Therefore, 721 = 204 + 195 + x. Solving for x, we get x = 721 - 204 - 195 = 322m. ### Answer: 322m
Expected answer: 322
Correct? Yes
Problem: An equilateral triangle has a perimeter of 201m. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 201/3 = <<201/3=67>>67m is the length of each side. ### Answer: 67 **Final Answer:** The total number of clips sold by Natalia in April and May is 72. The length of each side of an equilateral triangle with a perimeter of 201m is 67m.
Expected answer: 67
Correct? Yes
Problem: A large equilateral triangle has a perimeter of 756m. Find the length of each of its sides.
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 756 = 3s. 3s = 756. s = 252m. ### Answer: 252m
Expected answer: 252
Correct? Yes
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 7B:
Reasoning: The perimeter is the sum of the lengths of the three sides. Therefore, the length of the third side is 923 - 735 - 144 = 43m. ### Answer: 43m
Expected answer: 44
Correct? No
Problem: An equilateral triangle has a perimeter of 813 cm. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 813/3 = <<813/3=271>>271 cm is the length of each side. ### Answer: 271
Expected answer: 271
Correct? Yes
Problem: An equilateral triangle has a perimeter of 834 feet. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 834/3 = <<834/3=278>>278 feet is the length of each side. ### Answer: 278
Expected answer: 278
Correct? Yes
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 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. If the perimeter is 105m and all sides are equal, then each side must be 105/3 = 35m long. ### Answer: 35m
Expected answer: 35
Correct? Yes
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 7B:
Reasoning: The perimeter is the sum of the lengths of the three sides. Therefore, the length of each side is 195/3 = <<195/3=65>>65cm. ### Answer: 65
Expected answer: 65
Correct? Yes
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 7B:
Reasoning: The perimeter is the sum of the lengths of the three sides. We know that the first two sides are 350m and 154m long, so the third side must be 919 - 350 - 154 = 415m long. ### Answer: 415
Expected answer: 415
Correct? Yes
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 7B:
Reasoning: The perimeter is the sum of the lengths of the three sides. Therefore, 989 = 128 + 288 + x. x = 989 - 128 - 288 = 563m. ### Answer: 563m
Expected answer: 573
Correct? No
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 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, the length of each side is 321/3 = 107 meters. ### Answer: 107
Expected answer: 107
Correct? Yes
Problem: An equilateral triangle has a perimeter of 258 cm. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 258 = 3s. 3s = 258. s = 86. ### Answer: 86 **Note:** This is just an example of how I will solve the problem. You can replace "Natalia sold" and "An equilateral triangle has a perimeter of" with your own problem statements.
Expected answer: 86
Correct? Yes
Problem: An equilateral triangle has a perimeter of 75m. What is the length of each side of the triangle?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, the length of each side of the triangle is 75/3 = 25m. ### Answer: 25m
Expected answer: 25
Correct? Yes
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 7B:
Reasoning: The perimeter is the sum of the lengths of the three sides. 620 + 80 = 700m. Therefore, the length of the third side is 700 - 620 = 80m. ### Answer: 80m
Expected answer: 279
Correct? No
Problem: An equilateral triangle has a perimeter of 966 meters. What is the length of each side of this triangle?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, the length of each side of the triangle is 966/3 = 322 meters. ### Answer: 322
Expected answer: 322
Correct? Yes
Problem: An equilateral triangle has a perimeter of 486 cm. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 486 = 3s. 3s = 486. s = 162. ### Answer: 162 **Note:** This is just an example of how I will solve the problem. You can replace "Natalia sold clips to 48 of her friends in April, and then she sold half as many clips in May" with your own problem.
Expected answer: 162
Correct? Yes
Problem: An equilateral triangle has a perimeter of 948 meters. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 948/3 = <<948/3=316>>316 meters is the length of each side. ### Answer: 316
Expected answer: 316
Correct? Yes
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 7B:
Reasoning: The total perimeter is the sum of the length of the three sides. 252 + 687 = 939m. The third side is 998 - 939 = 59m. ### Answer: 59m
Expected answer: 59
Correct? Yes
Problem: An equilateral triangle has a perimeter of 618m. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 618 = 3s. 3s = 618. s = 206m. ### Answer: 206m
Expected answer: 206
Correct? Yes
Problem: An equilateral triangle has a perimeter of 483 meters. How long is each side?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 483/3 = <<483/3=161>>161 meters is the length of each side. ### Answer: 161
Expected answer: 161
Correct? Yes
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 7B:
Reasoning: The perimeter is the sum of the lengths of the three sides. 804 = 262 + 90 + x. Therefore, x = 804 - 262 - 90 = 452m. ### Answer: 452m
Expected answer: 452
Correct? Yes
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 7B:
Reasoning: The perimeter is the sum of the lengths of the three sides. Therefore, 925 = 183 + 498 + x. Substituting the values of 183 and 498 into the equation, we get 925 - 183 - 498 = x. Solving for x, we get x = 244m. ### Answer: 244
Expected answer: 244
Correct? Yes
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 7B:
Reasoning: The total perimeter is the sum of the lengths of the three sides. Therefore, 573 = 103 + 386 + x. Substituting these values into the equation, we get 573 = 489 + x. Subtracting 489 from both sides, we get x = 84. ### Answer: 84
Expected answer: 84
Correct? Yes
Problem: An equilateral triangle has a perimeter of 330m. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 330 = 3s. 3s = 330. s = 110. ### Answer: 110m
Expected answer: 110
Correct? Yes
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 7B:
Reasoning: The perimeter is the sum of the lengths of the three sides. 57 + 426 = 483m. Therefore, the length of the third side is 850 - 483 = 367m. ### Answer: 367
Expected answer: 367
Correct? Yes
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 7B:
Reasoning: The perimeter is the sum of the lengths of the three sides. Therefore, 764 = 265 + 56 + x. x = 764 - 265 - 56 = 443m. ### Answer: 443m
Expected answer: 443
Correct? Yes
Problem: An equilateral triangle has a perimeter of 723cm. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 723/3 = <<723/3=241>>241cm is the length of each side. ### Answer: 241
Expected answer: 241
Correct? Yes
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 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its sides. 315m + 100m = 415m. Therefore, the length of the third side is 738 - 415 = 323m. ### Answer: 323
Expected answer: 323
Correct? Yes
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 7B:
Reasoning: The perimeter is the sum of the lengths of the three sides. 762 = 131 + 147 + x. Therefore, x = 762 - 131 - 147 = 486m. ### Answer: 486m
Expected answer: 484
Correct? No
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 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. If the sum of two sides is 472m and the perimeter is 784m, then the third side must be 784 - 472 = 312m. ### Answer: 312
Expected answer: 312
Correct? Yes
Problem: An equilateral triangle has a perimeter of 543mm. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 543 = 3s. 3s = 543. s = 181mm. ### Answer: 181mm
Expected answer: 181
Correct? Yes
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 7B:
Reasoning: The perimeter of a triangle is equal to the sum of the length of its sides. Therefore, 867 = 287 + 475 + x. 287 + 475 = 867 - x. x = 867 - 287 - 475 = 74. ### Answer: 74
Expected answer: 105
Correct? No
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 7B:
Reasoning: The perimeter is the sum of the lengths of the three sides. If the other two sides add up to 838m and the perimeter is 934m, then the third side must be 934 - 838 = 96m. ### Answer: 96
Expected answer: 96
Correct? Yes
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 7B:
Reasoning: The perimeter is the sum of the lengths of the three sides. Therefore, 677 = 109 + 530 + x. Substituting the values of 109 and 530 into the equation, we get 677 = 639 + x. Subtracting 639 from both sides, we get x = 38m. ### Answer: 38m
Expected answer: 38
Correct? Yes
Problem: An equilateral triangle has a perimeter of 582 cm. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 582/3 = <<582/3=194>>194 cm is the length of each side. ### Answer: 194
Expected answer: 194
Correct? Yes
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 7B:
Reasoning: The perimeter is the sum of the lengths of the three sides of a triangle. We know that the largest side is 259m long and one other side is 11m long. So, the length of the last side must be 499 - 259 - 11 = 141m. ### Answer: 141
Expected answer: 229
Correct? No
Problem: An equilateral triangle has a perimeter of 966m. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 966/3 = <<966/3=322>>322m is the length of each side. ### Answer: 322
Expected answer: 322
Correct? Yes
Problem: An equilateral triangle has a perimeter of 894 inches. What is the length of each side of the triangle?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 894/3 = <<894/3=298>>298 inches is the length of each side of the triangle. ### Answer: 298
Expected answer: 298
Correct? Yes
Problem: An equilateral triangle has a perimeter of 891cm. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 891 = 3s. 3s = 891, so s = 297. ### Answer: 297
Expected answer: 297
Correct? Yes
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 7B:
Reasoning: The perimeter is the sum of the length of the three sides. Therefore, 762 = 122 + 245 + x. Where x is the length of the third side. 122 + 245 + x = 762 x = 762 - 122 - 245 x = 393 ### Answer: 393
Expected answer: 395
Correct? No
Problem: An equilateral triangle has a perimeter of 411m. What is the length of each side of the triangle?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, the length of each side of the triangle is 411/3 = 137m. ### Answer: 137m
Expected answer: 137
Correct? Yes
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 7B:
Reasoning: The total length of the sides is 72m, therefore each side of the triangle is 72/3 = 24m long. ### Answer: 24m
Expected answer: 24
Correct? Yes
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 7B:
Reasoning: The perimeter is the sum of the lengths of the three sides. Therefore, 537 + 68 = 605 meters. The remaining side must measure 605 - 537 = 68 meters. ### Answer: 68 **Note:** This is just an example of how I would solve the problem. You may not need to include all of the reasoning if you are confident in your ability to solve the problem.
Expected answer: 325
Correct? No
Problem: An equilateral triangle has a perimeter of 657 meters. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 657/3 = <<657/3=219>>219 meters is the length of each side. ### Answer: 219
Expected answer: 219
Correct? Yes
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 7B:
Reasoning: The perimeter of a scalene triangle is the sum of the lengths of its three sides. Therefore, the length of the third side is 909 - 368 - 230 = 311m. ### Answer: 311 **Note:** This is just an example of how I will solve the problem. The actual problem and answer may vary.
Expected answer: 311
Correct? Yes
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 7B:
Reasoning: The perimeter is the sum of the lengths of the three sides. 140 + 525 = 665m. The third side is 665 - 140 - 525 = 60m long. ### Answer: 60m
Expected answer: 35
Correct? No
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 7B:
Reasoning: The perimeter is the sum of the lengths of the three sides of a triangle. Therefore, 915 = 484 + 130 + x. x = 915 - 484 - 130 = 201cm. ### Answer: 201 **Note:** This is just an example of how I will solve the problem. I will not necessarily solve the problem in the exact same way as you. However, I will always explain my reasoning clearly and format my final answer in the same way.
Expected answer: 301
Correct? No
Problem: An equilateral triangle has a perimeter of 120 cm. How long is each side of the triangle?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 120 = 3s. 3s = 120. s = 40. ### Answer: 40 **Note:** This is just an example of how you should format your response. You can use your own unique style and wording, but the final answer should always be formatted as shown above.
Expected answer: 40
Correct? Yes
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 7B:
Reasoning: The perimeter is equal to the sum of the lengths of the three sides. Therefore, 661 = 382 + 151 + x. Substituting the known values into the equation, we get 661 = 382 + 151 + x. Solving for x, we get x = 661 - 382 - 151 = 128m. ### Answer: 128m
Expected answer: 128
Correct? Yes
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 7B:
Reasoning: The total perimeter is the sum of the lengths of the three sides. Therefore, the length of the third side is 678 - 419 - 164 = 678 - 583 = 95 feet. ### Answer: 95 **Note:** This is just an example of how I would solve the problem. You can replace the above text with your own problem and solution.
Expected answer: 95
Correct? Yes
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 7B:
Reasoning: The perimeter is the sum of the lengths of the three sides. 186 + 37 = 223m. Therefore, the length of the remaining side is 248 - 223 = 25m. ### Answer: 25m
Expected answer: 25
Correct? Yes
Problem: An equilateral triangle has a perimeter of 246 centimeters. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 246/3 = <<246/3=82>>82 centimeters is the length of each side. ### Answer: 82 **Final Answer:** The total number of clips sold by Natalia in April and May is 72. The length of each side of an equilateral triangle with a perimeter of 246 centimeters is 82 centimeters.
Expected answer: 82
Correct? Yes
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 7B:
Reasoning: The total perimeter is the sum of the lengths of the three sides. 180 + 338 = 518 meters. Therefore, the length of the third side is 518 - 180 - 338 = 40 meters. ### Answer: 40 meters
Expected answer: 221
Correct? No
Problem: An equilateral triangle has a perimeter of 684cm. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 684 = 3s. 3s = 684. s = 228. ### Answer: 228 **Note:** This is just an example of how I will solve the problem. You can replace "Natalia sold clips to 48 of her friends in April, and then she sold half as many clips in May" with your own problem.
Expected answer: 228
Correct? Yes
Problem: An equilateral triangle has a perimeter of 537m. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 537 = 3x + 2x. 3x + 2x = 537. 5x = 537. x = 537/5 = <<537/5=107>>107m for each side. ### Answer: 107
Expected answer: 179
Correct? No
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 7B:
Reasoning: The perimeter is the sum of the lengths of the three sides. Therefore, 568 = 110 + 205 + x. x = 568 - 110 - 205 = 253m. ### Answer: 253m
Expected answer: 253
Correct? Yes
Problem: An equilateral triangle has a perimeter of 942mm. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 942 = 3s. 3s = 942. s = 942/3 = 314mm. ### Answer: 314 **Note:** This is just an example of how I would solve the problem. You may not need to include all of the reasoning if you are confident in your ability to solve the problem.
Expected answer: 314
Correct? Yes
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 7B:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its sides. 325 + 15 = 340 meters. Therefore, the length of the third side is 633 - 340 = 293 meters. ### Answer: 293
Expected answer: 293
Correct? Yes
Problem: An equilateral triangle has a perimeter of 504 meters. What is the length of each side of the triangle?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 504 = 3s. 3s = 504. s = 168. ### Answer: 168
Expected answer: 168
Correct? Yes
Problem: An equilateral triangle has a perimeter of 51 cm. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 51 = 3s. 3s = 51, so s = 17 cm. ### Answer: 17 **Note:** This is just an example of how you should format your response. You can use your own unique style and wording, but the final answer should always be formatted as shown above.
Expected answer: 17
Correct? Yes
Problem: An equilateral triangle has a perimeter of 501 feet. What is the length of each side of the triangle?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, the length of each side of the triangle is 501/3 = 166.66 feet. ### Answer: 166.66
Expected answer: 167
Correct? No
Problem: The perimeter of an equilateral triangle is 411 meters. What is the length of each side of the triangle?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is the sum of the lengths of its three sides. Therefore, the length of each side of the triangle is 411/3 = 137 meters. ### Answer: 137
Expected answer: 137
Correct? Yes
Problem: An equilateral triangle has a perimeter of 114cm. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, the length of each side is 114/3 = 38cm. ### Answer: 38
Expected answer: 38
Correct? Yes
Problem: An equilateral triangle has a perimeter of 69m. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 69m = 3s. 3s = 69m, so s = 23m. ### Answer: 23m
Expected answer: 23
Correct? Yes
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 7B:
Reasoning: The total perimeter is the sum of the lengths of the three sides. Therefore, the length of the third side is 907 - 464 - 377 = 66m. ### Answer: 66 **Note:** This is just an example of how I would solve the problem. You may not need to include all of the reasoning if you are confident in your ability to solve the problem.
Expected answer: 66
Correct? Yes
Problem: An equilateral triangle has a perimeter of 966m. What is the length of each of its sides?
Gemma 7B:
Reasoning: The perimeter of an equilateral triangle is equal to the sum of the lengths of its sides. Therefore, 966 = 3s. 3s = 966. s = 966/3 = 322m. ### Answer: 322m
Expected answer: 322
Correct? Yes