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 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 3s = 990 cm. Dividing both sides by 3, we get s = 330 cm. ### Answer: 330
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 2B:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 2 + 667 = 997. ### Answer: 997
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 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 579 = 3s. Solving for s, we get s = 193 cm. ### Answer: 193
Expected answer: 193
Correct? Yes
Problem: An equilateral triangle has a perimeter of 684m. What is the length of each of its sides?
Gemma 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 684 = 3s. Solving for s, we get s = 228. ### 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 2B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. 503 = 223 + 46. Therefore, the length of the remaining side is 503 - 223 = <<503-223=280>>280 meters.
Expected answer: 234
Correct? No
Problem: An equilateral triangle has a perimeter of 105m. What is the length of each of its sides?
Gemma 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 105 = 3s. Solving for s, we get s = 35. Therefore, the length of each side of the equilateral triangle is 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 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 306 = 3s. Solving for s, we get s = 102cm. ### Answer: 102
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 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 33 = 3s. Solving for s, we get s = 11 cm. ### Answer: 11 cm
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 2B:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 861 = 192 + 159. Solving for the third side, we get 861 = 192 + 159. Therefore, the length of the third side is 861 - 192 - 159 = 612m.
Expected answer: 510
Correct? No
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: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, the length of one side is 489/3 = <<489/3=163>>163 centimeters.
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 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 696 = 3s. Solving for s, we get s = 232. ### 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 2B:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 804 = 180 + 579. Solving for the third side, we get 804 = 180 + 579. Therefore, the length of the third side is 639m.
Expected answer: 45
Correct? No
Problem: An equilateral triangle has a perimeter of 915cm. What is the length of each of its sides?
Gemma 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 3s = 915 cm. Dividing both sides by 3, we get s = 305 cm. ### Answer: 305
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 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 564 = 3s. Solving for s, we get s = 184 cm. ### Answer: 184
Expected answer: 188
Correct? No
Problem: An equilateral triangle has a perimeter of 594 cm. What is the length of each of its sides?
Gemma 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 594 = 3s. Solving for s, we get s = 198 cm. ### 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 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 453 = 3s. Solving for s, we get s = 151 cm. ### Answer: 151
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 2B:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 250 + 435 = 685. The length of the third side is 685m.
Expected answer: 213
Correct? No
Problem: An equilateral triangle has a total perimeter of 405 cm. Can you determine the length of each side?
Gemma 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 405 = 3s. Solving for s, we get s = 405 รท 3 = <<135>>135 cm. ### Answer: 135
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 2B:
Reasoning: The perimeter of an equilateral triangle is always equal to 3 times the length of one side. Therefore, the length of each side is 612/3 = <<612/3=204>>204 meters.
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 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 591 = 3s. Solving for s, we get s = 197 cm. ### Answer: 197
Expected answer: 197
Correct? Yes
Problem: An equilateral triangle has a perimeter of 858m. What is the length of each of its sides?
Gemma 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 858 = 3s. Solving for s, we get s = 286. ### 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 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 543 = 3s. Solving for s, we get s = 181 meters. ### 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 2B:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, the length of each side is 255/3 = <<255/3=85>>85 meters.
Expected answer: 85
Correct? Yes
Problem: An equilateral triangle has a perimeter of 570mm. Find the length of each side of this triangle.
Gemma 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 570 = 3s. Solving for s, we get s = 190. Therefore, the length of each side of the equilateral triangle is 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 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 129 = 3s. Solving for s, we get s = 43. Therefore, the length of each side of the equilateral triangle is 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 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 858 = 3s. Solving for s, we get s = 286. ### 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 2B:
### Answer: 151 km
Expected answer: 171
Correct? No
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:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 105 + 434 = 539. The third side is 539 meters long.
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 2B:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 37 + 559 = 773. The length of the third side is 773 - 37 = <<773-37=736>>736 cm.
Expected answer: 177
Correct? No
Problem: An equilateral triangle has a perimeter of 714m. What is the length of each of its sides?
Gemma 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 714 = 3s. Solving for s, we get s = <<714/3>> = 241m. ### Answer: 241
Expected answer: 238
Correct? No
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: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 147 + 590 = 792. The length of the third side is 792 - 147 = <<792-147=645>>645m.
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 2B:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 871 = 321 + 528. Solving for the third side, we get 871 = 849. ### Answer: 22
Expected answer: 22
Correct? Yes
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:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Therefore, 424 + 246 = 670. The length of the third side is 670m.
Expected answer: 321
Correct? No
Problem: An equilateral triangle has a perimeter of 936m. How long is each side of the triangle?
Gemma 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 3s = 936, which implies that s = 312. Therefore, each side of the equilateral triangle is 312m long.
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 2B:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 721 = 204 + 195. Solving for the third side, we get 721 = 204 + 195. Therefore, the length of the third side is 721 - 204 - 195 = 522m.
Expected answer: 322
Correct? No
Problem: An equilateral triangle has a perimeter of 201m. What is the length of each of its sides?
Gemma 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 201 = 3s. Solving for s, we get s = 67. ### Answer: 67
Expected answer: 67
Correct? Yes
Problem: A large equilateral triangle has a perimeter of 756m. Find the length of each of its sides.
Gemma 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 3s = 756, which gives s = <<756/3>>252. Therefore, the length of each side of the triangle is 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 2B:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 923 = 735 + 144. Solving for the third side, we get 144 = 923 - 735. ### Answer: 144
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 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 813 = 3s. Solving for s, we get s = 271 cm. ### 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 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 834 = 3s. Solving for s, we get s = 278 feet. ### 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 2B:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, the length of one side of the triangle is 105/3 = <<105/3=35>>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 2B:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, the length of each side is 195/3 = <<195/3=65>>65cm.
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 2B:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 919 = 350 + 154. Solving for the third side, we get 919 = 504. ### 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 2B:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 989 = 128 + 288. Solving for the third side, we get 288 = 989 - 128. Therefore, the length of the third side is 860m.
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 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 321 = 3s. Dividing both sides by 3, we get s = <<321/3=107>>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 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 258 = 3s. Solving for s, we get s = 258 รท 3 = <<86>>86 cm. ### Answer: 86
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 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 75 = 3s. Solving for s, we get s = 25. ### Answer: 25
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 2B:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 979 = 620 + 80. ### Answer: 879
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 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 966 = 3s. Solving for s, we get s = 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 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 486 = 3s. Solving for s, we get s = 486 รท 3 = <<162>>162 cm. ### Answer: 162
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 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 948 = 3s. Solving for s, we get s = 324. ### Answer: 324
Expected answer: 316
Correct? No
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:
Reasoning: The perimeter of a scalene triangle is equal to the sum of the lengths of its three sides. Therefore, the length of the third side is 998 - 252 - 687 = 649m.
Expected answer: 59
Correct? No
Problem: An equilateral triangle has a perimeter of 618m. What is the length of each of its sides?
Gemma 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 618 = 3s. Solving for s, we get s = 206. ### Answer: 206
Expected answer: 206
Correct? Yes
Problem: An equilateral triangle has a perimeter of 483 meters. How long is each side?
Gemma 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 483 = 3s. Solving for s, we get s = 483 รท 3 = <<161>>161 meters.
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 2B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Therefore, 804 = 262 + 90. Solving for the third side, we get 804 - 262 - 90 = 552. ### Answer: 552
Expected answer: 452
Correct? No
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: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 183 + 498 = 681. The length of the third side is 681m.
Expected answer: 244
Correct? No
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:
Reasoning: The perimeter of a scalene triangle is equal to the sum of the lengths of its three sides. Therefore, 573 = 103 + 386. Solving for the third side, we get 386 = 573 - 103. Therefore, the length of the third side is 483m.
Expected answer: 84
Correct? No
Problem: An equilateral triangle has a perimeter of 330m. What is the length of each of its sides?
Gemma 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 330 = 3s. Solving for s, we get s = 110. ### Answer: 110
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 2B:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 57 + 426 = 483m.
Expected answer: 367
Correct? No
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:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 764 = 265 + 56. Solving for the third side, we get 764 - 265 = 599. ### Answer: 599
Expected answer: 443
Correct? No
Problem: An equilateral triangle has a perimeter of 723cm. What is the length of each of its sides?
Gemma 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 723 = 3s. Solving for s, we get s = 241 cm. ### 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 2B:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 315 + 100 = 738. The length of the third side is 738 - 315 = <<738-315=423>>423m.
Expected answer: 323
Correct? No
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: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 762 = 131 + 147. Solving for the third side, we get 762 = 278. ### Answer: 484
Expected answer: 484
Correct? Yes
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:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, the third side must be 784 - 472 = <<784-472=312>>312m.
Expected answer: 312
Correct? Yes
Problem: An equilateral triangle has a perimeter of 543mm. What is the length of each of its sides?
Gemma 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 543 = 3s. Solving for s, we get s = 181. ### Answer: 181
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 2B:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 287 + 475 = 867. The length of the third side is 867 - 287 = <<867-287=580>>580m.
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 2B:
Reasoning: Let x be the length of the third side. Then the two known sides are 828m and 10m. The perimeter is 934m, so we have: x + 828m + 10m = 934m x = 934m - 828m - 10m = <<104m>>104m The length of the third side is 104m.
Expected answer: 96
Correct? No
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:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 109 + 530 = 677. ### Answer: 677
Expected answer: 38
Correct? No
Problem: An equilateral triangle has a perimeter of 582 cm. What is the length of each of its sides?
Gemma 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 582 = 3s. Solving for s, we get s = 194 cm. ### 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 2B:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. 499 = 259 + 11 The length of the last side is 499 - 259 - 11 = <<499-259-11=239>>239m.
Expected answer: 229
Correct? No
Problem: An equilateral triangle has a perimeter of 966m. What is the length of each of its sides?
Gemma 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 966 = 3s. Solving for s, we get s = 322. ### 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 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 894 = 3s. Solving for s, we get s = 294. ### Answer: 294
Expected answer: 298
Correct? No
Problem: An equilateral triangle has a perimeter of 891cm. What is the length of each of its sides?
Gemma 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 891 = 3s. Solving for s, we get 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 2B:
Reasoning: The perimeter of a triangle is the sum of the lengths of its three sides. Therefore, 122 + 245 = <<122+245=367>>367 meters.
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 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 411 = 3s. Solving for s, we get s = 411/3 = <<137>>137. ### Answer: 137
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 2B:
Reasoning: The sides of the triangle are equal in length. Each side = 72/3 = <<72/3=24>>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 2B:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 537 + 68 = 605. The length of the third side is 605 meters.
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 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 657 = 3s. Solving for s, we get s = 219. ### 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 2B:
Reasoning: The perimeter of a scalene triangle is equal to the sum of the lengths of its three sides. Therefore, 368 + 230 = 909. The length of the third side is 909 - 368 = <<909-368=541>>541m.
Expected answer: 311
Correct? No
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:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 700 = 140 + 525. Solving for the third side, we get 700 = 665. ### Answer: 35
Expected answer: 35
Correct? Yes
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:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 484 + 130 = 915. The length of the third side is 915 - 484 = <<915-484=431>>431cm.
Expected answer: 301
Correct? No
Problem: An equilateral triangle has a perimeter of 120 cm. How long is each side of the triangle?
Gemma 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 120 = 3s. Solving for s, we get s = 40 cm. ### Answer: 40
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 2B:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 382 + 151 = 533. The length of the third side is 533m.
Expected answer: 128
Correct? No
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:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 419 + 164 = 678. ### Answer: 678
Expected answer: 95
Correct? No
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 equal to the sum of the lengths of its three sides. Therefore, 248 = 186 + 37. Hence, the length of the remaining side is 248 - 186 = <<248-186=62>>62m.
Expected answer: 25
Correct? No
Problem: An equilateral triangle has a perimeter of 246 centimeters. What is the length of each of its sides?
Gemma 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 246 = 3s. Solving for s, we get s = 246 รท 3 = 82 cm. ### Answer: 82
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 2B:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 180 + 338 = 518. The length of the third side is 518 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 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 684 = 3s. Solving for s, we get s = 228. ### Answer: 228
Expected answer: 228
Correct? Yes
Problem: An equilateral triangle has a perimeter of 537m. What is the length of each of its sides?
Gemma 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 537 = 3s. Solving for s, we get s = 179. ### Answer: 179
Expected answer: 179
Correct? Yes
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:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 568 = 110 + 205. Solving for the third side, we get 358 = 205. ### Answer: 358
Expected answer: 253
Correct? No
Problem: An equilateral triangle has a perimeter of 942mm. What is the length of each of its sides?
Gemma 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 942 = 3s. Solving for s, we get s = 314. ### Answer: 314
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 2B:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 325 + 15 = 633. The length of the third side is 633 - 325 = <<633-325=308>>308 meters.
Expected answer: 293
Correct? No
Problem: An equilateral triangle has a perimeter of 504 meters. What is the length of each side of the triangle?
Gemma 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 504 = 3s. Solving for s, we get s = 168 meters. ### 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 2B:
Reasoning: The perimeter of an equilateral triangle is given by P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 51 = 3s. Solving for s, we get s = 17 cm. ### Answer: 17 cm
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 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 501 = 3s. Solving for s, we get s = 167 feet. ### Answer: 167
Expected answer: 167
Correct? Yes
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 given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 411 = 3s. Solving for s, we get s = 411/3 = <<140.33>>140.33 meters. ### Answer: 140.33
Expected answer: 137
Correct? No
Problem: An equilateral triangle has a perimeter of 114cm. What is the length of each of its sides?
Gemma 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 114 = 3s. Solving for s, we get s = 114/3 = <<34>>34 cm. ### Answer: 34
Expected answer: 38
Correct? No
Problem: An equilateral triangle has a perimeter of 69m. What is the length of each of its sides?
Gemma 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 69 = 3s. Solving for s, we get s = 23m. ### Answer: 23
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 2B:
Reasoning: The perimeter of a triangle is equal to the sum of the lengths of its three sides. Therefore, 464 + 377 = 907. The length of the third side is 907 - 464 = <<907-464=443>>443m.
Expected answer: 66
Correct? No
Problem: An equilateral triangle has a perimeter of 966m. What is the length of each of its sides?
Gemma 2B:
Reasoning: The perimeter of an equilateral triangle is given by the formula P = 3s, where P is the perimeter and s is the length of each side. Substituting the values, we get 966 = 3s. Solving for s, we get s = 322. ### Answer: 322
Expected answer: 322
Correct? Yes