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?
InternLM-Math Base 7B:
Reasoning: The perimeter of the triangle is 3 times the length of one of its sides.
Expected answer: 330
Correct? No
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?
InternLM-Math Base 7B:
Expected answer: 328
Correct? No
Problem: An equilateral triangle has a perimeter of 579 cm. What is the length of each of its sides?
InternLM-Math Base 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of a side. 579/3 = <<579/3=193>>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?
InternLM-Math Base 7B:
Reasoning: 684/3 = <<684/3=228>>228m The length of each of the sides is 228m. ### 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?
InternLM-Math Base 7B:
Expected answer: 234
Correct? No
Problem: An equilateral triangle has a perimeter of 105m. What is the length of each of its sides?
InternLM-Math Base 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of a side. So 105m/3 = <<105m/3=35>>35m is the length of a side. ### Answer: 35
Expected answer: 35
Correct? Yes
Problem: An equilateral triangle has a perimeter of 306cm. What is the length of each of its sides?
InternLM-Math Base 7B:
Reasoning: 306/3 = <<306/3=102>>102. The length of each of the sides of the equilateral triangle is 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?
InternLM-Math Base 7B:
Reasoning: 33/3 = <<33/3=11>>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?
InternLM-Math Base 7B:
Reasoning: 192+159+<<192+159=351>>351 = 861 The length of the third side is 192+159-<<192+159=351>>351 = 192+159-351 = 30m
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?
InternLM-Math Base 7B:
Expected answer: 163
Correct? No
Problem: An equilateral triangle has a perimeter of 696 meters. What is the length of each side of this triangle?
InternLM-Math Base 7B:
Reasoning: 696/3 = <<696/3=232>>232 The length of each side of the triangle is 232 meters.
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?
InternLM-Math Base 7B:
Reasoning: The sum of the lengths of the three sides of a triangle is 180m+180m+579m = <<180+180+579=1039>>1039m. The sum of the lengths of the two known sides of the triangle is 180m+579m = <<180+579=759>>759m. The sum of the lengths of the two known sides of the triangle is 759m, and the sum of the lengths of all three sides of the triangle is 1039m. The length of the third side of the triangle is 1039m โ 759m = <<1039-759=280>>280m. ### Answer: 280
Expected answer: 45
Correct? No
Problem: An equilateral triangle has a perimeter of 915cm. What is the length of each of its sides?
InternLM-Math Base 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of a side. 3 times 915/3 = 3*<<915/3=305>>305 = 915.
Expected answer: 305
Correct? No
Problem: An equilateral triangle has a perimeter of 564 cm. What is the length of each of its sides?
InternLM-Math Base 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of a side.
Expected answer: 188
Correct? No
Problem: An equilateral triangle has a perimeter of 594 cm. What is the length of each of its sides?
InternLM-Math Base 7B:
Reasoning: The sum of the three side lengths of an equilateral triangle is 594. The three side lengths are the same. The three side lengths are 594/3 = <<594/3=198>>198.
Expected answer: 198
Correct? Yes
Problem: An equilateral triangle has a perimeter of 453 cm. How long is each side of the triangle?
InternLM-Math Base 7B:
Reasoning: 453/3 = <<453/3=151>>151. The length of each side of the triangle is 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?
InternLM-Math Base 7B:
Reasoning: The sum of the two given side lengths is 250m+435m= <<250m+435m=685m>>685m. The sum of the three side lengths is 898m. The sum of the two given side lengths and the length of the third side is 685m+<<the length of the third side>>=898m. Therefore, the length of the third side of the triangle is 898m-685m= <<898m-685m=213m>>213m. ### Answer: 213
Expected answer: 213
Correct? Yes
Problem: An equilateral triangle has a total perimeter of 405 cm. Can you determine the length of each side?
InternLM-Math Base 7B:
Reasoning: 405 รท 3 = <<405 รท 3=135>>135. The length of each side of the equilateral triangle is 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?
InternLM-Math Base 7B:
Reasoning: The total perimeter of the equilateral triangle = 612 meters. The length of each side of the equilateral triangle = 612/3 = 204 meters. ### Answer: 204
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?
InternLM-Math Base 7B:
Reasoning: The length of each side of the triangle is 1/3 of the perimeter. 1/3 of 591 = 197. ### 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?
InternLM-Math Base 7B:
Reasoning: The length of each of the sides of the equilateral triangle is 858/3 = <<858/3=286>>286m. ### 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?
InternLM-Math Base 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of a side. So 3 times the length of a side is 543. 3 times the length of a side is 3 <<3*543/3=543>>543. The length of a side is 543/3 = <<543/3=181>>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?
InternLM-Math Base 7B:
Reasoning: The length of each side of the triangle is 255/3 = <<255/3=85>>85 meters. ### 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.
InternLM-Math Base 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of the 3 sides. The length of each side of the triangle is 570/3 = <<570/3=190>>190mm. ### Answer: 190
Expected answer: 190
Correct? Yes
Problem: An equilateral triangle has a perimeter of 129m. What is the length of each of its sides?
InternLM-Math Base 7B:
Reasoning: 3x = 129m. x = 129/3 = <<129/3=43>>43m. The length of each of the sides of the equilateral triangle is 43m. ### Answer: 43
Expected answer: 43
Correct? Yes
Problem: An equilateral triangle has a perimeter of 858 meters. What is the length of each of its sides?
InternLM-Math Base 7B:
Reasoning: 3s = 858. s = 858/3 = <<858/3=286>>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?
InternLM-Math Base 7B:
Reasoning: 513/3 = <<513/3=171>>171 The length of each side of the triangle is 171 km.
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?
InternLM-Math Base 7B:
Reasoning: The two sides of the field that are 105 and 434 meters long are the two shorter sides. The third side of the field is the longest side. The two shorter sides of the field add up to 105+434 = <<105+434=539>>539 meters. The sum of the two longer sides of the field is 828-539 = <<828-539=289>>289 meters. The two longer sides of the field are 289/2 = <<289/2=144.5>>144.5 meters long. The third side of the field is 144.5+144.5 = <<144.5+144.5=289>>289 meters long. ### Answer: 289
Expected answer: 289
Correct? Yes
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?
InternLM-Math Base 7B:
Reasoning: The sum of the two given sides is 37+559=<<37+559=596>>596 cm. Since the sum of the three sides of a triangle is equal to the perimeter, the length of the third side is 773-596=<<773-596=177>>177 cm. ### Answer: 177
Expected answer: 177
Correct? Yes
Problem: An equilateral triangle has a perimeter of 714m. What is the length of each of its sides?
InternLM-Math Base 7B:
Reasoning: 714/3 = <<714/3=238>>238m ### 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?
InternLM-Math Base 7B:
Reasoning: 147+590+<<the length of the third side>>=792 The length of the third side = 792-147-590 = 55m ### Answer: 55
Expected answer: 55
Correct? Yes
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?
InternLM-Math Base 7B:
Reasoning: The sum of the lengths of the other two sides is 321+528= <<321+528=849>>849 meters. The sum of the three sides is 871 meters. The sum of the lengths of the other two sides is 849/2= <<849/2=424.5>>424.5 meters. The length of the third side is 871-424.5= <<871-424.5=446.5>>446.5 meters. ### Answer: 446.5
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.
InternLM-Math Base 7B:
Reasoning: The sum of the lengths of the two sides of a triangle is always greater than the length of the third side.
Expected answer: 321
Correct? No
Problem: An equilateral triangle has a perimeter of 936m. How long is each side of the triangle?
InternLM-Math Base 7B:
Reasoning: 3s=936 s= <<3s=936>> 936/3 = 312 ### Answer: 312
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?
InternLM-Math Base 7B:
Reasoning: The sum of the lengths of the other two sides of the triangle is 204+195 = <<204+195=399>>399m. The sum of the three side lengths of a triangle is 2 times the length of the third side. The length of the third side of the triangle is 399/2 = <<399/2=199.5>>199.5m. ### Answer: 199.5
Expected answer: 322
Correct? No
Problem: An equilateral triangle has a perimeter of 201m. What is the length of each of its sides?
InternLM-Math Base 7B:
Reasoning: 201/3 = <<201/3=67>>67m ### 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.
InternLM-Math Base 7B:
Reasoning: The length of each side of the equilateral triangle is 756/3 = <<756/3=252>>252m. ### Answer: 252
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?
InternLM-Math Base 7B:
Reasoning: The sum of the 3 sides of a triangle is 923m. The other two sides are 735m and 144m. The sum of the other two sides is 735m+144m= <<735m+144m=879m>>879m. The length of the third side is 923m-879m= <<923m-879m=44m>>44m. ### Answer: 44
Expected answer: 44
Correct? Yes
Problem: An equilateral triangle has a perimeter of 813 cm. What is the length of each of its sides?
InternLM-Math Base 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of a side. 3x = 813. 3x/3 = 813/3. x = 271. ### 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?
InternLM-Math Base 7B:
Reasoning: 3x = 834 x = 834/3 x = <<834/3=278>>278 The length of each of its sides is 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?
InternLM-Math Base 7B:
Reasoning: 105/3 = <<105/3=35>>35 ### 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?
InternLM-Math Base 7B:
Reasoning: 195/3 = <<195/3=65>>65. The length of each side is 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?
InternLM-Math Base 7B:
Reasoning: The sum of the other two sides is 350+154 = <<350+154=504>>504m. The other side is 919-504 = <<919-504=415>>415m. ### 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?
InternLM-Math Base 7B:
Reasoning: The sum of the two given sides is 128m+288m=416m. The sum of the three sides is 989m. The length of the third side is 989m-416m=<<989m-416m=573m>>573m. ### Answer: 573
Expected answer: 573
Correct? Yes
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?
InternLM-Math Base 7B:
Reasoning: 321/3 = <<321/3=107>>107 The length of each side of the triangle is 107 meters.
Expected answer: 107
Correct? Yes
Problem: An equilateral triangle has a perimeter of 258 cm. What is the length of each of its sides?
InternLM-Math Base 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of a side.
Expected answer: 86
Correct? No
Problem: An equilateral triangle has a perimeter of 75m. What is the length of each side of the triangle?
InternLM-Math Base 7B:
Reasoning: The perimeter of the triangle is 75m. The length of each side of the triangle is 75m/3 = <<75m/3=25>>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?
InternLM-Math Base 7B:
Reasoning: The sum of the two sides of a triangle is greater than the third side. 620+80 = <<620+80=700>>700m. The length of the third side is 979-700 = <<979-700=279>>279m. ### Answer: 279
Expected answer: 279
Correct? Yes
Problem: An equilateral triangle has a perimeter of 966 meters. What is the length of each side of this triangle?
InternLM-Math Base 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of a side. So, 3 times the length of a side is 966. Divide 966 by 3 to get the length of a side. 966/3 = <<966/3=322>>322. The length of a side is 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?
InternLM-Math Base 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of a side. 3 times 486/3 = <<3*486/3=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?
InternLM-Math Base 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of a side. So 3 times the length of a side is 948. 3 times the length of a side is 3x. 3x = 948. x = 948/3. x = 948/3 = <<948/3=316>>316. The length of each of the sides is 316 meters.
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?
InternLM-Math Base 7B:
You are a mathematics teacher that solves all problems correctly and explains your reasoning. Write your final answer in the last line of your response. The last line should always be formatted as follows: "### Answer: <<your final answer here.>>".
Expected answer: 59
Correct? No
Problem: An equilateral triangle has a perimeter of 618m. What is the length of each of its sides?
InternLM-Math Base 7B:
Reasoning: The length of each of the sides of the equilateral triangle is 618/3 = <<618/3=206>>206m. ### Answer: 206
Expected answer: 206
Correct? Yes
Problem: An equilateral triangle has a perimeter of 483 meters. How long is each side?
InternLM-Math Base 7B:
Reasoning: 483/3 = <<483/3=161>>161. Each side of the equilateral triangle is 161 meters long. ### 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?
InternLM-Math Base 7B:
Reasoning: The sum of the other two sides is 262+90 = 352m. The sum of the other two sides is 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are 352m. The other two sides, 262m and 90m, are
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?
InternLM-Math Base 7B:
Reasoning: The sum of the three sides of a triangle is 183+498+<<183+498=681>>681m. The length of the third side is 925-<<183+498=681>>681m = 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?
InternLM-Math Base 7B:
Reasoning: The sum of the lengths of the other two sides of the triangle is 573-103-386 = 184m. The length of the third side is 184m.
Expected answer: 84
Correct? No
Problem: An equilateral triangle has a perimeter of 330m. What is the length of each of its sides?
InternLM-Math Base 7B:
Reasoning: 3x = 330 x = 330/3 x = <<330/3=110>>110m ### 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?
InternLM-Math Base 7B:
Reasoning: The sum of the lengths of the other two sides of a triangle is always greater than the length of the third side. The sum of the lengths of the other two sides of the given triangle is 57m+426m= <<57m+426m=483m>>483m. The length of the third side of the given triangle is <<483m-57m=426m>>426m. ### Answer: 426
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?
InternLM-Math Base 7B:
Expected answer: 443
Correct? No
Problem: An equilateral triangle has a perimeter of 723cm. What is the length of each of its sides?
InternLM-Math Base 7B:
Reasoning: The length of each of the sides of the equilateral triangle is 723/3 = <<723/3=241>>241cm. ### 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?
InternLM-Math Base 7B:
Reasoning: The sum of the lengths of the 3 sides of a triangle is 738m. The first 2 sides of the triangle have a length of 100m and 315m. The 3rd side of the triangle is 738m โ 100m โ 315m = <<738m โ 100m โ 315m=323m>>323m. ### Answer: 323m
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?
InternLM-Math Base 7B:
Reasoning: The sum of the lengths of the other two sides of a triangle is greater than the length of the third side. The other two sides of the triangle are 131m and 147m. 131m+147m= <<131m+147m=278m>>278m. 131m<278m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m. 131m<147m.
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?
InternLM-Math Base 7B:
Reasoning: The sum of the other two sides is 472m. The other two sides are 472m-<x>m=<<472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m-<x>m=472m
Expected answer: 312
Correct? No
Problem: An equilateral triangle has a perimeter of 543mm. What is the length of each of its sides?
InternLM-Math Base 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of a side. 543/3 = <<543/3=181>>181. The length of each of the sides of the equilateral triangle is 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?
InternLM-Math Base 7B:
Reasoning: The first and second side lengths are <<287m+475m=762m>>762m. The sum of the first, second, and third side lengths is 867m. The sum of the first and second side lengths is 762m. The third side length is 867m-762m = 105m. ### Answer: 105
Expected answer: 105
Correct? Yes
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?
InternLM-Math Base 7B:
Reasoning: The other side of the triangle is <<10m.>>. The sum of the three sides of the triangle is 934m. The sum of the other two sides is 838m. 934m-838m= <<96m.>>. The length of the third side of the triangle is <<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?
InternLM-Math Base 7B:
Reasoning: The sum of the two given sides is 109+530 = 639m. The sum of the three sides of a triangle is 3 times the sum of the two given sides. The length of the third side is 3*639/3 = <<3*639/3=639>>639m. ### Answer: 639
Expected answer: 38
Correct? No
Problem: An equilateral triangle has a perimeter of 582 cm. What is the length of each of its sides?
InternLM-Math Base 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of a side. So 582/3 = <<582/3=194>>194 is the length of a side of the triangle. ### 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?
InternLM-Math Base 7B:
You are a mathematics teacher that solves all problems correctly and explains your reasoning. Write your final answer in the last line of your response. The last line should always be formatted as follows: "### Answer: <<your final answer here.>>".
Expected answer: 229
Correct? No
Problem: An equilateral triangle has a perimeter of 966m. What is the length of each of its sides?
InternLM-Math Base 7B:
Expected answer: 322
Correct? No
Problem: An equilateral triangle has a perimeter of 894 inches. What is the length of each side of the triangle?
InternLM-Math Base 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of a side. 894/3 = <<894/3=298>>298. The length of a side of the equilateral triangle is 298 inches.
Expected answer: 298
Correct? Yes
Problem: An equilateral triangle has a perimeter of 891cm. What is the length of each of its sides?
InternLM-Math Base 7B:
Reasoning: 891/3 = <<891/3=297>>297 The length of each of the sides of the equilateral triangle is 297cm.
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?
InternLM-Math Base 7B:
Yes. The sum of the two given side lengths is 122+245 = 367 meters. The sum of the three side lengths is 762 meters. The sum of the other two side lengths is 762-367 = 395 meters. The length of the third side is 395-367 = 28 meters. ### Answer: 28
Expected answer: 395
Correct? No
Problem: An equilateral triangle has a perimeter of 411m. What is the length of each side of the triangle?
InternLM-Math Base 7B:
Reasoning: The length of each side of the triangle is 411/3 = <<411/3=137>>137m. ### 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?
InternLM-Math Base 7B:
Reasoning: The total length of the three sides of the triangle is 3x = 72m. So, the length of each side of the triangle is 72m/3 = <<72m/3=24m>>24m. ### 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?
InternLM-Math Base 7B:
Expected answer: 325
Correct? No
Problem: An equilateral triangle has a perimeter of 657 meters. What is the length of each of its sides?
InternLM-Math Base 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of a side. 3x = 657. x = 657/3 = <<657/3=219>>219. The length of each of the three sides of the equilateral triangle is 219 meters.
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?
InternLM-Math Base 7B:
Reasoning: The perimeter of a triangle is the sum of the lengths of the three sides. The sum of the lengths of the first two sides is 368m+230m= <<368m+230m=598m>>598m. The sum of the lengths of the first two sides and the length of the third side is 909m. The length of the third side is 909m-598m= <<909m-598m=311m>>311m. ### Answer: 311
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?
InternLM-Math Base 7B:
Reasoning: The two given sides of the triangle are 140m and 525m. The sum of the 3 sides of a triangle is the perimeter. The sum of the 3 sides of the triangle is 140m + 525m + 700m = 1165m. The 3rd side of the triangle is 1165m โ 140m โ 525m = <<1165 โ 140 โ 525 = 500>>500m. ### Answer: 500
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?
InternLM-Math Base 7B:
Reasoning: The sum of the two given sides of the triangle is 484+130 = 614. The sum of the three sides of the triangle is 915. The sum of the first two sides of the triangle is 614. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and third sides of the triangle is 915. The sum of the first and
Expected answer: 301
Correct? No
Problem: An equilateral triangle has a perimeter of 120 cm. How long is each side of the triangle?
InternLM-Math Base 7B:
Expected answer: 40
Correct? No
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?
InternLM-Math Base 7B:
Reasoning: The other side of the field is 661-382-151 = 28m.
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?
InternLM-Math Base 7B:
Reasoning: The two given sides of the triangle are 419 and 164. The sum of the two given sides is 419+164 = <<419+164=583>>583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet. The sum of the two given sides is 583 feet.
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?
InternLM-Math Base 7B:
The sum of the two given sides is 186+37= <<186+37=223>>223m. The other side must be 248-223= <<248-223=25>>25m long.
Expected answer: 25
Correct? Yes
Problem: An equilateral triangle has a perimeter of 246 centimeters. What is the length of each of its sides?
InternLM-Math Base 7B:
Reasoning: The length of each of the sides of the equilateral triangle is 246/3 = <<246/3=82>>82 centimeters. ### 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.
InternLM-Math Base 7B:
Reasoning: The sum of the three sides of a triangle is 180+338+<<the length of the third side>>=739. The length of the third side is 739-180-338=<<739-180-338=221>>221. ### Answer: 221
Expected answer: 221
Correct? Yes
Problem: An equilateral triangle has a perimeter of 684cm. What is the length of each of its sides?
InternLM-Math Base 7B:
Reasoning: The perimeter of an equilateral triangle is 684/3 = <<684/3=228>>228 centimeters. The length of each of the three sides of the equilateral triangle is 228/3 = <<228/3=76>>76 centimeters.
Expected answer: 228
Correct? No
Problem: An equilateral triangle has a perimeter of 537m. What is the length of each of its sides?
InternLM-Math Base 7B:
Reasoning: 3x= <<3x=3x>> 3x=537 3x/3=537/3 x= <<3x/3=537/3 3x/3=179 3x/3=179 x=179>> 179m ### 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?
InternLM-Math Base 7B:
Reasoning: The other two sides of the triangle are 110m and 205m. The sum of the other two sides is 110m+205m=<<110m+205m=315m>>315m. The other two sides add to 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides is 315m. The sum of the other two sides
Expected answer: 253
Correct? No
Problem: An equilateral triangle has a perimeter of 942mm. What is the length of each of its sides?
InternLM-Math Base 7B:
Reasoning: The perimeter of an equilateral triangle is 3 times the length of a side. 942/3 = <<942/3=314>>314. The length of each of the sides of the equilateral triangle is 314mm.
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?
InternLM-Math Base 7B:
Reasoning: 15+15+325=<<15+15+325=350>>350 The other side of the garden is 350-15-15=<<350-15-15=320>>320 meters long. ### Answer: 320
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?
InternLM-Math Base 7B:
Reasoning: 504/3 = <<504/3=168>>168 The length of each side of the triangle is 168 meters.
Expected answer: 168
Correct? Yes
Problem: An equilateral triangle has a perimeter of 51 cm. What is the length of each of its sides?
InternLM-Math Base 7B:
Reasoning: The length of each of the 3 sides of the equilateral triangle is 51/3 = <<51/3=17>>17 cm. ### Answer: 17
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?
InternLM-Math Base 7B:
Reasoning: The length of each side of the triangle is 501/3 = <<501/3=167>>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?
InternLM-Math Base 7B:
Reasoning: The length of each side of the triangle is 411/3 = <<411/3=137>>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?
InternLM-Math Base 7B:
Expected answer: 38
Correct? No
Problem: An equilateral triangle has a perimeter of 69m. What is the length of each of its sides?
InternLM-Math Base 7B:
Reasoning: 69/3 = <<69/3=23>>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?
InternLM-Math Base 7B:
Reasoning: The sum of the first two sides of the triangle is 464+377 = 841m. The sum of the first two sides is 907m - 841m = <<907-841=66>>66m less than the total perimeter of the triangle. Therefore, the length of the third side of the triangle is 66m. ### Answer: 66
Expected answer: 66
Correct? Yes
Problem: An equilateral triangle has a perimeter of 966m. What is the length of each of its sides?
InternLM-Math Base 7B:
Reasoning: 3s = 966m s = 966/3 = <<966/3=322>>322m ### Answer: 322m
Expected answer: 322
Correct? Yes