Common Core Standard 3.MD.D.8-quadrilateral
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: The perimeter of a rectangular swimming pool is 324 meters. The length of the pool is 83 meters. What is the width of the pool?
InternLM-Math Base 7B:
Reasoning: The width of the pool is 324-2*83 = <<324-2*83=59>>59 meters. ### Answer: 59
Expected answer: 79
Correct? No
Problem: A square has a perimeter of 40m. What is the length of each side?
InternLM-Math Base 7B:
Reasoning: The length of each side of the square is 10m.
Expected answer: 10
Correct? Yes
Problem: A square has a perimeter of 344m. What is the length of each side of the square?
InternLM-Math Base 7B:
Reasoning: The length of each side of the square is 344/4 = <<344/4=86>>86m. ### Answer: 86
Expected answer: 86
Correct? Yes
Problem: A square has a perimeter of 348m. What would be the length of each side of the square?
InternLM-Math Base 7B:
Reasoning: The length of each side of the square is 348/4 = <<348/4=87>>87m. ### Answer: 87
Expected answer: 87
Correct? Yes
Problem: A rectangle has a perimeter of 194 cm. The length of one of its sides is 49 cm. Can you determine the length of its other side?
InternLM-Math Base 7B:
Yes. The other side of the rectangle is <<194-49=145>>145 cm.
Expected answer: 48
Correct? No
Problem: A square has a perimeter of 192m. What is the length of one side?
InternLM-Math Base 7B:
Reasoning: The length of one side is 192/4 = 48m. ### Answer: 48
Expected answer: 48
Correct? Yes
Problem: A square has a perimeter of 68cm. What is the length of one side?
InternLM-Math Base 7B:
Reasoning: 68/4 = <<68/4=17>>17 ### Answer: 17
Expected answer: 17
Correct? Yes
Problem: A rectangle has a perimeter of 52 meters. If one of the sides measures 4 meters, how long is the other side?
InternLM-Math Base 7B:
Reasoning: 4+4+<<2x=52>>2x+2x = 52. 2x=<<2x/2=x=26>>26. The other side is 26 meters.
Expected answer: 22
Correct? No
Problem: A quadrilateral has a perimeter of 229m. Two sides of the quadrilateral have lengths of 93m and 98m respectively. The third side of the quadrilateral is 36m long. What is the length of the fourth side?
InternLM-Math Base 7B:
Reasoning: The first two sides of the quadrilateral are 93m and 98m. The sum of the first two sides is <<93m+98m=191m>>191m. The sum of the first two sides and the third side is 93m+98m+36m= <<93m+98m+36m=227m>>227m. The sum of the first two sides and the third side is 227m. The sum of the first two sides and the third side and the fourth side is 229m. The sum of the first two sides and the third side and the fourth side is 227m+1m. 1m is the length of the fourth side. ### Answer: 1
Expected answer: 2
Correct? No
Problem: The perimeter of a square is 16m. What is the length of each side of this square?
InternLM-Math Base 7B:
Reasoning: The length of each side of the square is 16/4 = <<16/4=4>>4m. ### Answer: 4
Expected answer: 4
Correct? Yes
Problem: A square has a perimeter of 272m. What is the length of each side of the square?
InternLM-Math Base 7B:
Reasoning: The length of each side of the square is 272/4 = <<272/4=68>>68m. ### Answer: 68
Expected answer: 68
Correct? Yes
Problem: A square has a perimeter of 244m. What is the length of each side of the square?
InternLM-Math Base 7B:
Reasoning: The length of each side of the square is 244/4 = <<244/4=61>>61m. ### Answer: 61
Expected answer: 61
Correct? Yes
Problem: A quadrilateral has a perimeter of 227m. The lengths of three of its sides are 70m, 29m, and 61m. What is the length of the fourth side of the quadrilateral?
InternLM-Math Base 7B:
Reasoning: The sum of the three given side lengths is 70+29+61= <<70+29+61=160>>160m. The sum of the four side lengths of the quadrilateral is 227m. The length of the fourth side of the quadrilateral is 227-160= <<227-160=67>>67m. ### Answer: 67
Expected answer: 67
Correct? Yes
Problem: A square has a perimeter of 280m. What is the length of the side of that square?
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: 70
Correct? No
Problem: A quadrilateral has a perimeter of 219cm. Two of its sides have lengths of 37cm and 98cm, and a third side is known to be 41cm. How long is the fourth side?
InternLM-Math Base 7B:
Reasoning: The sum of the lengths of the first three sides is 37+98+41 = 176. The sum of the lengths of the first three sides and the length of the fourth side is 219. The length of the fourth side is 219-176 = <<219-176=43>>43.
Expected answer: 43
Correct? Yes
Problem: A square has a perimeter of 44m. Can you calculate the length of one side?
InternLM-Math Base 7B:
Reasoning: The length of one side is 11m. ### Answer: 11
Expected answer: 11
Correct? Yes
Problem: A rectangular garden has a perimeter of 282 meters. The longer side measures 71 meters. What is the length of the shorter side?
InternLM-Math Base 7B:
Reasoning: The length of the shorter side is 282-71-71 = <<282-71-71=140>>140 meters. ### Answer: 140
Expected answer: 70
Correct? No
Problem: A rectangular garden has a total perimeter of 128 meters. If the shorter side of the garden has a length of 57 meters, how long is the other side?
InternLM-Math Base 7B:
Reasoning: The other side of the garden is 128-57-57 = <<128-57-57=14>>14 meters. ### Answer: 14
Expected answer: 7
Correct? No
Problem: A square has a perimeter of 392m. What is the length of each side of the square?
InternLM-Math Base 7B:
Reasoning: The length of each side of the square is 392/4 = <<392/4=98>>98m. ### Answer: 98
Expected answer: 98
Correct? Yes
Problem: A rectangle has a perimeter of 204m. If one of its sides has a length of 16m, what is the length of the other side?
InternLM-Math Base 7B:
Reasoning: The other side has a length of <<204-16-16=172/2=86>>86m. ### Answer: 86
Expected answer: 86
Correct? Yes
Problem: A square has a perimeter of 336cm. What is the length of one of its sides?
InternLM-Math Base 7B:
Reasoning: A square has 4 equal sides. The length of one of its sides is 336/4 = <<336/4=84>>84cm. ### Answer: 84
Expected answer: 84
Correct? Yes
Problem: A square has a perimeter of 144 meters. What is the length of one side of the square?
InternLM-Math Base 7B:
Reasoning: The length of one side of the square is 144/4 = 36. ### Answer: 36
Expected answer: 36
Correct? Yes
Problem: A quadrilateral has a perimeter of 236 cm. Two of its sides measure 69 cm and 50 cm respectively, and a third side measures 39 cm. What is the length of the fourth side?
InternLM-Math Base 7B:
Reasoning: The sum of the first three sides of the quadrilateral is 69+50+39 = 158. The sum of the first three sides and the fourth side is 236. The length of the fourth side is 236-158 = <<236-158=78>>78. ### Answer: 78
Expected answer: 78
Correct? Yes
Problem: A quadrilateral has a perimeter of 193cm. Two of its sides measure 37cm and 14cm, while the other two sides measure 73cm and an unknown length. What is the length of the side of the quadrilateral that is unknown?
InternLM-Math Base 7B:
Reasoning: The other two sides of the quadrilateral are 37+14= <<37+14=51>>51cm and 73+<<37+14=51>><<73+51=124>>124cm. The perimeter of the quadrilateral is 37+14+73+<<37+14=51>><<73+51=124>>124= <<37+14+73+124=193>>193cm. The other two sides of the quadrilateral are 37+14= <<37+14=51>>51cm and 73+<<37+14=51>><<73+51=124>>124cm. The perimeter of the quadrilateral is 37+14+73+<<37+14=51>><<73+51=124>>124= <<37+14+73+124=193>>193cm. ### Answer: 51
Expected answer: 69
Correct? No
Problem: A square has a perimeter of 160m. What is the length of one of its sides?
InternLM-Math Base 7B:
Reasoning: 160/4 = <<160/4=40>>40m.
Expected answer: 40
Correct? Yes
Problem: A rectangle has a perimeter of 228 meters. The length of the rectangle is 90 meters. What is the width of the rectangle?
InternLM-Math Base 7B:
Reasoning: The width of the rectangle is 228-2*90 = 48 meters. ### Answer: 48
Expected answer: 24
Correct? No
Problem: The perimeter of a square field is 136 meters. Given that all sides are equal in a square, What is the length of one side of the field?
InternLM-Math Base 7B:
Reasoning: The perimeter of a square is 4 times the length of a side. 136/4= <<136/4=34>>34. The length of a side of the field is 34 meters. ### Answer: 34
Expected answer: 34
Correct? Yes
Problem: A rectangle has a total perimeter of 236 meters. If one side of the rectangle is 43 meters, can you determine the length of the opposite side?
InternLM-Math Base 7B:
Reasoning: The other side of the rectangle is 236 43 = <<236 43=193>>193 meters.
Expected answer: 75
Correct? No
Problem: A quadrilateral has a perimeter of 206m. Two of its sides together have a length of 58m, and the other two sides together have a length of 54m and 1m, respectively. What is the length of the missing portion of the perimeter?
InternLM-Math Base 7B:
Reasoning: The two sides that are 54m and 1m are opposite. The two sides that are 58m are not opposite. The missing portion of the perimeter is 206m-58m-54m-1m= <<206m-58m-54m-1m=93m>>93m. ### Answer: 93m
Expected answer: 93
Correct? Yes
Problem: A square field has a total perimeter of 284 meters. How long is each side of the square field?
InternLM-Math Base 7B:
Reasoning: The total perimeter of a square is 4 times the length of one side. So, 284/4 = <<284/4=71>>71 meters is the length of one side of the square field. ### Answer: 71
Expected answer: 71
Correct? Yes
Problem: A rectangle has a perimeter of 150 feet. If the length of the rectangle is 69 feet, what is the width of the rectangle?
InternLM-Math Base 7B:
Reasoning: The width of the rectangle is 150-69 = <<150-69=81>>81 feet. ### Answer: 81
Expected answer: 6
Correct? No
Problem: The perimeter of a rectangle is 166m. If one of the sides measures 35m, how long is the other side?
InternLM-Math Base 7B:
Reasoning: The other side of the rectangle is <<166-35-35=96>>96m.
Expected answer: 48
Correct? No
Problem: A square has a perimeter of 124m. What is the length of each side?
InternLM-Math Base 7B:
Reasoning: The length of each side of a square is the same. The perimeter of a square is 4 times the length of a side. 124/4 = <<124/4=31>>31m. The length of each side of the square is 31m.
Expected answer: 31
Correct? Yes
Problem: A rectangular field has a perimeter of 336 feet. The length of one of its sides is 79 feet. What is the length of the opposite side?
InternLM-Math Base 7B:
Expected answer: 89
Correct? No
Problem: A square plot of land has a perimeter of 132 meters. What is the length of one side of the square?
InternLM-Math Base 7B:
Reasoning: The perimeter of a square is 4 times the length of a side. 132/4 = <<132/4=33>>33 The length of one side of the square is 33 meters. ### Answer: 33
Expected answer: 33
Correct? Yes
Problem: A rectangle has a perimeter of 138 feet. If the length of the rectangle is 46 feet, what is the width of the rectangle?
InternLM-Math Base 7B:
Reasoning: The width of the rectangle is 138-46 = <<138-46=92>>92 feet. ### Answer: 92
Expected answer: 23
Correct? No
Problem: A rectangular field has a total perimeter of 200 meters. The length of the field is known to be 49 meters. What is the width of the field in meters?
InternLM-Math Base 7B:
Reasoning: The width of the field is 200-49 = <<200-49=151>>151 meters. ### Answer: 151
Expected answer: 51
Correct? No
Problem: A square has a perimeter of 200m. What is the length of each side?
InternLM-Math Base 7B:
Reasoning: 200/4 = 50 The length of each side is 50m.
Expected answer: 50
Correct? Yes
Problem: A quadrilateral has a perimeter of 199m. The length of one side is 9m, the length of the second side is 30m, and the length of the third side is 71m. What is the length of the fourth side?
InternLM-Math Base 7B:
Reasoning: The sum of the lengths of the first three sides is 9m+30m+71m= <<9m+30m+71m=110m>>110m. The sum of the lengths of the first three sides and the length of the fourth side is 199m. Therefore, the length of the fourth side is 199m-110m= <<199m-110m=89m>>89m. ### Answer: 89
Expected answer: 89
Correct? Yes
Problem: A quadrilateral has a perimeter of 207m. The lengths of three of its sides are 35m, 62m and 70m respectively. What is the length of the fourth side?
InternLM-Math Base 7B:
Reasoning: The sum of the three given side lengths is <<35+62+70=167>>167m. The sum of the four side lengths is 207m. Therefore, the length of the fourth side is 207-167 = <<207-167=40>>40m. ### Answer: 40
Expected answer: 40
Correct? Yes
Problem: A rectangle has a perimeter of 384cm. If one of the shorter sides of the rectangle is measured to be 99cm, what would be the length of the longer sides of the rectangle?
InternLM-Math Base 7B:
Reasoning: The sum of the 4 sides of a rectangle is 384. The 2 shorter sides are 99. The 2 longer sides are 2(384-2(99))=2(384-198)=2(186)=<<2(186)=372>>372.
Expected answer: 93
Correct? No
Problem: A quadrilateral shape has a perimeter of 255 m. The first and the second sides have lengths of 78m and 15m respectively, while the third side has a length of 63m. What is the length of the fourth side?
InternLM-Math Base 7B:
Reasoning: The first, second, and third sides have a total length of 78m+15m+63m = <<78m+15m+63m=156m>>156m. The fourth side has a length of 255m-156m = <<255m-156m=99m>>99m. ### Answer: 99
Expected answer: 99
Correct? Yes
Problem: A square has a perimeter of 128m. What is the length of one of its sides?
InternLM-Math Base 7B:
Reasoning: The length of one of the square's sides is 128/4 = <<128/4=32>>32m. ### Answer: 32
Expected answer: 32
Correct? Yes
Problem: Imagine a rectangle with a perimeter of 96 feet. You know that one pair of opposite sides are each 33 feet long. Can you find the length of the other pair of opposite sides?
InternLM-Math Base 7B:
You can find the length of the other pair of sides by subtracting 33 from 48. 48-33=15. The other pair of sides is 15 feet long.
Expected answer: 15
Correct? Yes
Problem: The perimeter of a square field is 112 meters. What is the length of each side?
InternLM-Math Base 7B:
Reasoning: The length of each side of the square is 112/4 = <<112/4=28>>28 meters. ### Answer: 28
Expected answer: 28
Correct? Yes
Problem: The perimeter of a square is 32 cm. Can you find the length of one of its sides?
InternLM-Math Base 7B:
The length of one of the square's sides is 8 cm.
Expected answer: 8
Correct? Yes
Problem: A square has a perimeter of 364m. What is the length of each side of the square?
InternLM-Math Base 7B:
Reasoning: The length of each side of the square is 364/4 = <<364/4=91>>91m. ### Answer: 91
Expected answer: 91
Correct? Yes
Problem: The total perimeter of a rectangle is found to be 144 feet. The length of one side is known to be 38 feet. What is the length of the other side of the rectangle in feet?
InternLM-Math Base 7B:
Reasoning: The other side of the rectangle is 144-38 = <<144-38=106>>106 feet. ### Answer: 106
Expected answer: 34
Correct? No
Problem: A quadrilateral has a perimeter of 205m. Two of its sides add up to 54m and the other two sides add up to 22m and 37m respectively. What is the length of the remaining side to complete the perimeter?
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: 92
Correct? No
Problem: The perimeter of a rectangular field is 174m. If the length of the field is 65m, what is the width of the field?
InternLM-Math Base 7B:
Reasoning: The width of the field is 174-65 = <<174-65=109>>109m. ### Answer: 109
Expected answer: 22
Correct? No
Problem: A quadrilateral has a perimeter of 176 cm. The lengths of three sides are 25 cm, 17 cm and 89 cm respectively. What is the length of the fourth side?
InternLM-Math Base 7B:
Reasoning: The sum of the three given side lengths is <<25+17+89=121>>121 cm. The sum of the four side lengths is 176 cm. The length of the fourth side is 176 – 121 = 55. ### Answer: 55
Expected answer: 45
Correct? No
Problem: A square has a perimeter of 372 meters. What is the length of each side?
InternLM-Math Base 7B:
Reasoning: The length of each side of the square is 372/4 = <<372/4=93>>93 meters. ### Answer: 93
Expected answer: 93
Correct? Yes
Problem: A square field has a perimeter of 240 meters. Can you find out the length of one side of the field?
InternLM-Math Base 7B:
Reasoning: The length of one side of the field is 240/4 = <<240/4=60>>60 meters. ### Answer: 60
Expected answer: 60
Correct? Yes
Problem: The perimeter of a rectangle is 242 meters. Knowing that one of the sides of this rectangle is 97 meters, can you determine the length of the other side?
InternLM-Math Base 7B:
Reasoning: The other side of the rectangle is 242-97 = <<242-97=145>>145 meters. ### Answer: 145
Expected answer: 24
Correct? No
Problem: Tom has constructed a square with a total perimeter of 316 meters. Can you determine the length of each side of this square?
InternLM-Math Base 7B:
Reasoning: 316/4 = <<316/4=79>>79 The length of each side of the square is 79 meters.
Expected answer: 79
Correct? Yes
Problem: A square has a perimeter of 268cm. What is the length of each side of the square?
InternLM-Math Base 7B:
The length of each side of the square is 268/4 = 67cm.
Expected answer: 67
Correct? Yes
Problem: A square has a perimeter of 348m. What is the length of each side of the square?
InternLM-Math Base 7B:
Reasoning: The length of each side of the square is 348/4 = <<348/4=87>>87m. ### Answer: 87
Expected answer: 87
Correct? Yes
Problem: A square has a perimeter of 400m. What is the length of one of its sides?
InternLM-Math Base 7B:
Reasoning: The length of one of the square's sides is 400/4 = <<400/4=100>>100m. ### Answer: 100
Expected answer: 100
Correct? Yes
Problem: A quadrilateral has sides with lengths of 81m, 100m, and 19m. If its perimeter is 243m, what is the length of the fourth side?
InternLM-Math Base 7B:
Reasoning: 81+100+19+<<x>> = 243 <<x>> = 243-100-81-19 <<x>> = 41 ### Answer: 41
Expected answer: 43
Correct? No
Problem: A rectangle has a perimeter of 186cm. If one of its sides is 50cm long, how long is the other side?
InternLM-Math Base 7B:
Reasoning: The other side of the rectangle is 86/2 = <<86/2=43>>43cm long. ### Answer: 43
Expected answer: 43
Correct? Yes
Problem: A rectangle has a perimeter of 224 cm. If the length of one of its sides is 78 cm, what is the length of the adjacent side?
InternLM-Math Base 7B:
Reasoning: The other side of the rectangle is 78+78 = <<78+78=156>>156 cm.
Expected answer: 34
Correct? No
Problem: A quadrilateral has two sides measuring 79m and 97m. Another side measures 51m. The total perimeter of the quadrilateral is 235m. What is the length of the fourth side?
InternLM-Math Base 7B:
Reasoning: 79+97+51= <<79+97+51=227>>227 235-227= <<235-227=8>>8 The length of the fourth side is 8m. ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: A square has a perimeter of 28m. Can you calculate the length of one side of this square?
InternLM-Math Base 7B:
Reasoning: 28/4 = <<28/4=7>>7m ### Answer: 7
Expected answer: 7
Correct? Yes
Problem: A square has a perimeter of 48cm. What is the length of each side?
InternLM-Math Base 7B:
Reasoning: The length of each side is 12cm. ### Answer: 12
Expected answer: 12
Correct? Yes
Problem: A square plot of land has a perimeter of 184 meters. Can you find the length of one side of the plot?
InternLM-Math Base 7B:
Reasoning: 184/4 = <<184/4=46>>46. The length of one side of the plot is 46 meters. ### Answer: 46
Expected answer: 46
Correct? Yes
Problem: A square has a perimeter of 56 meters. What is the length of each side?
InternLM-Math Base 7B:
Reasoning: The length of each side is 56/4 = <<56/4=14>>14 meters. ### Answer: 14
Expected answer: 14
Correct? Yes
Problem: A quadrilateral has a perimeter of 157m. If one of its sides is 97m long, and the other two sides are 5m and 30m, respectively, what is the length of the fourth side to complete the perimeter?
InternLM-Math Base 7B:
Reasoning: The 5m, 30m, and 97m sides are the three sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of the fourth side are the four sides of the quadrilateral. The 5m, 30m, 97m, and the length of
Expected answer: 25
Correct? No
Problem: A quadrilateral has a perimeter of 173m. The length of the first side is 46m, second side is 50m and third side is 35m. What is the length of the fourth side?
InternLM-Math Base 7B:
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Expected answer: 42
Correct? No
Problem: A square has a perimeter of 72 cm. What is the length of one of its sides?
InternLM-Math Base 7B:
Reasoning: 72/4 = <<72/4=18>>18 ### Answer: 18
Expected answer: 18
Correct? Yes
Problem: A square has a perimeter of 352m. What is the length of each side of the square?
InternLM-Math Base 7B:
Reasoning: 352/4 = <<352/4=88>>88 The length of each side of the square is 88m.
Expected answer: 88
Correct? Yes
Problem: A rectangle has 23m for its length and has a total perimeter of 116m. What is the length of its width?
InternLM-Math Base 7B:
Reasoning: The width of the rectangle is 116-23-23 = <<116-23-23=70>>70m. ### Answer: 70
Expected answer: 35
Correct? No
Problem: A square has a perimeter of 124m. What is the length of each side?
InternLM-Math Base 7B:
Reasoning: The length of each side is 124/4 = 31m. ### Answer: 31
Expected answer: 31
Correct? Yes
Problem: A quadrilateral has a total perimeter of 131m. Three of its sides have lengths 24m, 57m, and 17m respectively. What is the length of the fourth side?
InternLM-Math Base 7B:
Reasoning: The sum of the 3 given side lengths is <<24+57+17=98>>98m. The sum of the 4 side lengths is 131m. Therefore, the length of the 4th side is 131-98= <<131-98=33>>33m. ### Answer: 33
Expected answer: 33
Correct? Yes
Problem: A rectangle has a perimeter of 254m. One of its sides has a length of 89m. What is the length of the other side?
InternLM-Math Base 7B:
Reasoning: The other side of the rectangle has a length of <<254-2*89=78>>78m. ### Answer: 78
Expected answer: 38
Correct? No
Problem: A square has a perimeter of 208m. What is the length of each side?
InternLM-Math Base 7B:
Reasoning: 208/4 = <<208/4=52>>52m ### Answer: 52
Expected answer: 52
Correct? Yes
Problem: A square has a perimeter of 64m. What is the length of each side of the square?
InternLM-Math Base 7B:
Reasoning: The length of each side of the square is 64/4 = <<64/4=16>>16m. ### Answer: 16
Expected answer: 16
Correct? Yes
Problem: A quadrilateral has a total perimeter of 196 meters. The lengths of three of its sides combined is 183 meters (with one side being 92 meters and the other two sides being 29 and 62 meters respectively). Can you figure out the length of the fourth side?
InternLM-Math Base 7B:
Reasoning: The sum of the three sides is 92+29+62 = 183. The fourth side is 196-183 = 13. ### Answer: 13
Expected answer: 13
Correct? Yes
Problem: The perimeter of a quadrilateral is 191 units. If one side is 35 units in length, another side is 76 units, and the third side is 5 units, what is the length of the fourth side in units?
InternLM-Math Base 7B:
Reasoning: The sum of the 4 sides of a quadrilateral is 191 units. 35+76+5= <<35+76+5=116>>116. 191-116= <<191-116=75>>75. The 4th side is 75 units in length. ### Answer: 75
Expected answer: 75
Correct? Yes
Problem: A square has a perimeter of 104m. What is the length of each side?
InternLM-Math Base 7B:
Reasoning: The length of each side of a square is 104/4 = <<104/4=26>>26m. ### Answer: 26
Expected answer: 26
Correct? Yes
Problem: The perimeter of a rectangle is 198 cm. If the length of this rectangle is 90 cm, what is the width?
InternLM-Math Base 7B:
Reasoning: The width of a rectangle is 198-2*90= <<198-2*90=18>>18 cm. ### Answer: 18
Expected answer: 9
Correct? No
Problem: Jack is designing a rectangular garden with a total perimeter of 128 feet. He has already planned for one pair of opposite sides to be 47 feet each. What should be the length of the remaining two opposite sides?
InternLM-Math Base 7B:
Reasoning: The length of the remaining two sides is 128-2*47= <<128-2*47=4>>4 feet. ### Answer: 4
Expected answer: 17
Correct? No
Problem: A square has a perimeter of 356m. What is the length of one of its sides?
InternLM-Math Base 7B:
Reasoning: The length of one of the square's sides is 356/4 = <<356/4=89>>89m. ### Answer: 89
Expected answer: 89
Correct? Yes
Problem: A quadrilateral has a perimeter of 236 units. Two sides of the quadrilateral measure 89 units and 87 units respectively, while the third side is 1 unit long. What is the length of the fourth side?
InternLM-Math Base 7B:
Expected answer: 59
Correct? No
Problem: A square has a perimeter of 340 meters. What is the length of each side of this square?
InternLM-Math Base 7B:
Reasoning: The length of each side of a square is the same. The perimeter of a square is 4 times the length of a side. 340/4 = <<340/4=85>>85 ### Answer: 85
Expected answer: 85
Correct? Yes
Problem: A square has a perimeter of 16m. What is the length of each side?
InternLM-Math Base 7B:
Reasoning: A square has 4 equal sides. 16/4 = <<16/4=4>>4m. The length of each side is 4m.
Expected answer: 4
Correct? Yes
Problem: A quadrilateral has four sides. The length of the first side is 1m, the second side is 54m, and the third side is 9m. The total perimeter of this quadrilateral is 81m. What would be the length of the fourth side in meters?
InternLM-Math Base 7B:
Reasoning: The sum of the first three side lengths is 1+54+9 = <<1+54+9=64>>64m. The sum of the first three side lengths and the length of the fourth side is 81m. The length of the fourth side is 81-64 = <<81-64=17>>17m. ### Answer: 17
Expected answer: 17
Correct? Yes
Problem: A quadrilateral, which is a perfect square, has a total perimeter of 316m. What is the length of each side of this square?
InternLM-Math Base 7B:
Expected answer: 79
Correct? No
Problem: A square has a perimeter of 300m. How long is each side of the square?
InternLM-Math Base 7B:
Reasoning: The square has 4 equal sides. The sum of the 4 sides is 300m. 300m/4 = <<300m/4=75>>75m. Each side of the square is 75m.
Expected answer: 75
Correct? Yes
Problem: A quadrilateral has a perimeter of 198m. Two of the sides have lengths of 19m and 57m respectively, another side is 22m, what is the length of the remaining side?
InternLM-Math Base 7B:
Reasoning: The sum of the lengths of the 4 sides of a quadrilateral is 198m. The sum of the lengths of 3 of the sides is 19m+57m+22m= <<19m+57m+22m=98m>>98m. The length of the remaining side is 198m-98m= <<198m-98m=100m>>100m. ### Answer: 100m
Expected answer: 100
Correct? Yes
Problem: A square has a perimeter of 172m. What is the length of each side of the square?
InternLM-Math Base 7B:
Reasoning: 172/4 = <<172/4=43>>43m ### Answer: 43
Expected answer: 43
Correct? Yes
Problem: A square has a perimeter of 304 cm. What is the length of one of its sides?
InternLM-Math Base 7B:
Reasoning: 304/4 = <<304/4=76>>76. The length of one of the square's sides is 76 cm.
Expected answer: 76
Correct? Yes
Problem: A rectangle has a total perimeter of 158 meters. Each of the shorter sides is 51 meters long. What is the length of each of the longer sides?
InternLM-Math Base 7B:
You can do this problem in two different ways. One way is to use a variable. The other way is to use a variable and a diagram.
Expected answer: 28
Correct? No
Problem: A square has a perimeter of 72m. What is the length of one its sides?
InternLM-Math Base 7B:
Reasoning: 4s=72, 4s/4=72/4, s=18, 18m ### Answer: 18m
Expected answer: 18
Correct? Yes
Problem: A rectangular playground is bordered by a fence. Two opposite sides of the fence are 19m each. If the total length of the fence is 166m, what is the length of each of the other two sides?
InternLM-Math Base 7B:
Reasoning: The length of each of the other two sides is 166-2x = <<166-2x=44>>44m. ### Answer: 44
Expected answer: 64
Correct? No
Problem: A quadrilateral has a perimeter of 246m. You know that two of its sides are 40m and 32m long, another side is 95m long. What is the length of the fourth side?
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: 79
Correct? No
Problem: A square has a perimeter of 32m. What is the length of one of its sides?
InternLM-Math Base 7B:
Reasoning: The length of one of the square's sides is 32/4 = <<32/4=8>>8m. ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: A square has a perimeter of 12 meters. Can you find the length of one side of the square?
InternLM-Math Base 7B:
Reasoning: The length of one side of the square is 12/4 = <<12/4=3>>3 meters. ### Answer: 3
Expected answer: 3
Correct? Yes
Problem: A quadrilateral has a perimeter of 160m. If the three known sides have lengths of 29m, 16m, and 41m, what is the length of the fourth side?
InternLM-Math Base 7B:
Reasoning: The sum of the three known side lengths is 29m+16m+41m=<<29m+16m+41m=86m>>86m. The sum of the three known side lengths, 86m, and the length of the fourth side, <<x>>, is 160m. Therefore, 86m+<<x>>=<<86m+x=160m>>160m. Subtract 86m from both sides. 86m-86m+<<x>>=<<x>>=160m-86m=<<x>>=<<74m>>74m. ### Answer: 74
Expected answer: 74
Correct? Yes
Problem: A rectangle has a perimeter of 98m. If one of its sides is 5m long, what is the length of the other side?
InternLM-Math Base 7B:
Reasoning: The other side is 98-5 = <<98-5=93>>93m long. ### Answer: 93
Expected answer: 44
Correct? No
Problem: A rectangle has two sides measuring 45m each. If the total perimeter of the rectangle is 210m, what is the length of each of the other two sides?
InternLM-Math Base 7B:
Reasoning: The other two sides of the rectangle are <<45*2=90>>90m each. ### Answer: 90
Expected answer: 60
Correct? No