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?
Mistral 7B:
Reasoning: The formula for the perimeter of a rectangle is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. We are given P = 324 and l = 83. Solving for w: 324 = 2(83) + 2w 324 = 166 + 2w 2(324 - 166) = 2w 158 = 2w w = 158 / 2 w = 79 ### Answer: 79
Expected answer: 79
Correct? Yes
Problem: A square has a perimeter of 40m. What is the length of each side?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 40m, then the length of one side is 40/4 = <<40/4=10>>10m. ### Answer: 10m
Expected answer: 10
Correct? Yes
Problem: A square has a perimeter of 344m. What is the length of each side of the square?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 344m, then the length of one side is 344/4 = <<344/4=86>>86m. ### Answer: 86m
Expected answer: 86
Correct? Yes
Problem: A square has a perimeter of 348m. What would be the length of each side of the square?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 348m, then the length of one side is 348/4 = <<348/4=87>>87m. ### Answer: 87m
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?
Mistral 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of all its sides. So, if we know the length of one side and the perimeter, we can find the length of the other side by subtracting the known values. The length of the other side is 194 - 49 = <<194-49=145>>145 cm. ### Answer: 145
Expected answer: 48
Correct? No
Problem: A square has a perimeter of 192m. What is the length of one side?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, the length of one side is 192/4 = <<192/4=48>>48m. ### Answer: 48m
Expected answer: 48
Correct? Yes
Problem: A square has a perimeter of 68cm. What is the length of one side?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 68cm, then the length of one side is 68/4 = <<68/4=17>>17cm. ### 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?
Mistral 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width. We know that P = 52 and l = 4. So, we can solve for w: 52 = 2(4) + 2w 52 = 8 + 2w 44 = 2w w = 22 ### Answer: 22 meters.
Expected answer: 22
Correct? Yes
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?
Mistral 7B:
Reasoning: Let's denote the length of the fourth side as x. The formula for the perimeter of a quadrilateral is the sum of the lengths of all its sides. So, we have: 93m + 98m + 36m + x = 229m Solving for x, we get: x = 229m - (93m + 98m + 36m) x = 229m - 227m x = 2m ### Answer: 2m
Expected answer: 2
Correct? Yes
Problem: The perimeter of a square is 16m. What is the length of each side of this square?
Mistral 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. So, the length of one side is the perimeter divided by 4. ### Answer: 4 (since 16/4 = 4)
Expected answer: 4
Correct? Yes
Problem: A square has a perimeter of 272m. What is the length of each side of the square?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 272m, then the length of one side is 272/4 = <<272/4=68>>68m. ### Answer: 68m
Expected answer: 68
Correct? Yes
Problem: A square has a perimeter of 244m. What is the length of each side of the square?
Mistral 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. So, the length of one side is the perimeter divided by 4. ### Answer: 61 cm (since 244/4 = 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?
Mistral 7B:
Reasoning: Let's denote the length of the fourth side as x. The sum of the lengths of all four sides of a quadrilateral is equal to its perimeter. So, we have: 70m + 29m + 61m + x = 227m x = 227m - (70m + 29m + 61m) x = 227m - 160m x = 67m ### Answer: 67m
Expected answer: 67
Correct? Yes
Problem: A square has a perimeter of 280m. What is the length of the side of that square?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 280m, then the length of one side is 280/4 = <<280/4=70>>70m. ### Answer: 70m
Expected answer: 70
Correct? Yes
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?
Mistral 7B:
Reasoning: Let's denote the length of the fourth side as x. The formula for the perimeter of a quadrilateral is the sum of the lengths of all its sides. So, we have: 37cm + 98cm + 41cm + x = 219cm Solving for x, we get: x = 219cm - (37cm + 98cm + 41cm) x = 219cm - 176cm x = 43cm ### Answer: 43cm
Expected answer: 43
Correct? Yes
Problem: A square has a perimeter of 44m. Can you calculate the length of one side?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 44m, then the length of one side is 44/4 = <<44/4=11>>11m. ### Answer: 11m
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?
Mistral 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2l + 2w, where l is the length of the longer side and w is the length of the shorter side. We are given that P = 282 and l = 71. Solving for w, we get: 282 = 2(71) + 2w 282 = 142 + 2w 282 - 142 = 2w 140 = 2w w = 140 / 2 w = 70 ### Answer: 70
Expected answer: 70
Correct? Yes
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?
Mistral 7B:
Reasoning: The formula for the perimeter of a rectangle is P = 2(L + W), where L is the length and W is the width. We know the perimeter (P) and one side (L), so we can solve for the other side (W). First, let's find the value of L in terms of W: L = 128 - 2(W) Now, we know that L = 57, so we can substitute this into the equation: 57 = 128 - 2(W) Solving for W: 2(W) = 128 - 57 W = (128 - 57) / 2 W = 63 / 2 W = 31.5 meters ### Answer: 31.5 meters
Expected answer: 7
Correct? No
Problem: A square has a perimeter of 392m. What is the length of each side of the square?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 392m, then the length of one side is 392/4 = <<392/4=98>>98m. ### Answer: 98m
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?
Mistral 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(L + W), where L is the length of one side and W is the width. We know that P = 204m and L = 16m. Solving for W, we get W = (P - 2L)/2 = (204 - 2*16)/2 = 96m. ### Answer: 96m
Expected answer: 86
Correct? No
Problem: A square has a perimeter of 336cm. What is the length of one of its sides?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, the length of one side is the perimeter divided by 4. ### Answer: 336/4 = 84cm. Or, if you prefer, the length of one side is the square root of the area (since the area of a square is side^2), and the area is the square of the side length. So, the length of one side is the square root of (336/4)^2 = 84cm. ### Answer: 84cm. Both answers are correct, but the first one is more straightforward and commonly used.
Expected answer: 84
Correct? Yes
Problem: A square has a perimeter of 144 meters. What is the length of one side of the square?
Mistral 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. So, the length of one side is the perimeter divided by 4. ### Answer: 36 (since 144/4 = 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?
Mistral 7B:
Reasoning: Let's denote the length of the fourth side as x. We know that the sum of the lengths of all four sides of a quadrilateral is equal to its perimeter. So, we have the following equation: 69 + 50 + 39 + x = 236 Solving for x: 69 + 50 + 39 + x = 236 x = 236 - (69 + 50 + 39) x = 236 - 158 x = 78 ### Answer: 78 CM.
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?
Mistral 7B:
Reasoning: Let the unknown side be x. The sum of the lengths of all sides of a quadrilateral is equal to its perimeter. So, we have the equation: 37 + 14 + 73 + x = 193. Solving for x, we get: x = 193 - (37 + 14 + 73) = 193 - 124 = 69. ### Answer: 69cm
Expected answer: 69
Correct? Yes
Problem: A square has a perimeter of 160m. What is the length of one of its sides?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 160m, then the length of one side is 160 / 4 = <<160/4=40>>40m. ### Answer: 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?
Mistral 7B:
Reasoning: The formula for the perimeter of a rectangle is P = 2l + 2w, where l is the length and w is the width. We are given that P = 228 and l = 90. Solving for w, we get: 228 = 2(90) + 2w 228 = 180 + 2w 2w = 48 w = 24 ### Answer: 24 utschke
Expected answer: 24
Correct? Yes
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?
Mistral 7B:
Reasoning: The perimeter of a square is calculated by multiplying the length of one side by 4. So, if the perimeter is 136 meters, then the length of one side is 136/4 = <<136/4=34>>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?
Mistral 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(L + W), where L is the length and W is the width. We know that P = 236 and L = 43. We can solve for W: W = (P - 2L) / 2 W = (236 - 2*43) / 2 W = 150 / 2 W = 75 ### Answer: 75 utschke
Expected answer: 75
Correct? Yes
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?
Mistral 7B:
Reasoning: Let's denote the length of the missing side as x. The sum of the lengths of all four sides of the quadrilateral is 206m. We know that the sum of the lengths of two sides is 58m + 54m + 1m = 113m, and the missing side is x. So, the equation for the perimeter is: Perimeter = 206m = 113m + x + x Solving for x: 206m - 113m - x - x = 0 206m - 2x = 113m 206 - 2 = 2/m (113/m) 2/m = 2/113 m = 113/2 x = 206 - 113/2 = 113/2 - 113/4 = 113/4 ### Answer: The length of the missing portion of the perimeter is 113/4 meters.
Expected answer: 93
Correct? No
Problem: A square field has a total perimeter of 284 meters. How long is each side of the square field?
Mistral 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. So, the length of one side is the perimeter divided by 4. ### Answer: 71 (rounded to the nearest whole number)
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?
Mistral 7B:
Reasoning: The formula for the perimeter of a rectangle is P = 2L + 2W, where L is the length and W is the width. We are given that P = 150 feet and L = 69 feet. Solving for W, we get: 150 = 2(69) + 2W 150 = 138 + 2W 2W = 150 - 138 2W = 12 W = 6 feet ### Answer: 6 feet
Expected answer: 6
Correct? Yes
Problem: The perimeter of a rectangle is 166m. If one of the sides measures 35m, how long is the other side?
Mistral 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of all four sides. Since we know one side and the perimeter, we can find the other three sides using the formula Perimeter = 2(Length + Width). We can rearrange this formula to find the width: Width = (Perimeter - 2(Length)) / 2. Let's plug in the given values: Width = (166 - 2(35)) / 2 = (166 - 70) / 2 = 96 / 2 = <<96/2=48>>48m. ### Answer: 48m
Expected answer: 48
Correct? Yes
Problem: A square has a perimeter of 124m. What is the length of each side?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 124m, then the length of one side is 124/4 = <<124/4=31>>31m. ### Answer: 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?
Mistral 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width. We know the perimeter and one side length, so we can solve for the width: 336 = 2(79) + 2w 336 = 158 + 2w 2w = 178 w = 89 feet The length of the opposite side is equal to the width, so the length of the opposite side is also 89 feet. ### Answer: 89 feet
Expected answer: 89
Correct? Yes
Problem: A square plot of land has a perimeter of 132 meters. What is the length of one side of the square?
Mistral 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. So, the length of one side is the perimeter divided by 4. ### Answer: 132/4=33 The length of one side of the square is 33 meters.
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?
Mistral 7B:
Reasoning: The formula for the perimeter of a rectangle is P = 2L + 2W, where L is the length and W is the width. We are given that P = 138 feet and L = 46 feet. Solving for W, we get: 138 = 2(46) + 2W 138 = 92 + 2W 2W = 138 - 92 2W = 46 W = 46 / 2 ### Answer: 23 feet
Expected answer: 23
Correct? Yes
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?
Mistral 7B:
Reasoning: The formula for the perimeter of a rectangle is P = 2(L+W), where L is the length and W is the width. We know the perimeter (P) and the length (L), so we can solve for the width (W): W = (P - 2L) / 2 W = (200 - 2*49) / 2 W = 100 / 2 W = 50 ### Answer: 50
Expected answer: 51
Correct? No
Problem: A square has a perimeter of 200m. What is the length of each side?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 200m, then the length of one side is 200/4 = <<200/4=50>>50m. ### Answer: 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?
Mistral 7B:
Reasoning: The sum of the lengths of all sides of a quadrilateral is equal to its perimeter. We know the lengths of three sides, so we can find the length of the fourth side by subtracting the sum of the lengths of the three known sides from the perimeter. Let x be the length of the fourth side. The sum of the lengths of the three known sides is 9 + 30 + 71 = 110m. The perimeter of the quadrilateral is 199m, so the length of the fourth side is 199 - 110 = <<199-110=89>>89m. ### Answer: 89m
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?
Mistral 7B:
Reasoning: Let's denote the length of the fourth side as x. The formula for the perimeter of a quadrilateral is the sum of the lengths of all its sides. So, we have: 35m + 62m + 70m + x = 207m x = 207m - (35m + 62m + 70m) x = 207m - 167m x = 40m ### Answer: 40m
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?
Mistral 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2l + 2w, where l is the length of the longer side and w is the width. We know that P = 384cm and w = 99cm. Solving for l: 384 = 2l + 2*99 384 - 198 = 2l 286 = 2l l = 143cm ### Answer: 143cm
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?
Mistral 7B:
Reasoning: Let's denote the length of the fourth side as x. The sum of the lengths of all sides of a quadrilateral is equal to its perimeter. So, we have: 78 + 15 + 63 + x = 255 Solving for x, we get: x = 255 - (78 + 15 + 63) x = 255 - 156 x = 99 ### Answer: 99 utsch!
Expected answer: 99
Correct? Yes
Problem: A square has a perimeter of 128m. What is the length of one of its sides?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 128m, then the length of one side 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?
Mistral 7B:
Reasoning: The sum of the lengths of all four sides of a rectangle is equal to its perimeter. Since we know the lengths of two opposite sides (33 feet each), we can find the lengths of the other two sides by subtracting the known lengths from the perimeter and dividing by 2 (since there are two unknown sides). Let's denote the length of the unknown sides as x. Then, the equation for the perimeter is: 33 + 33 + x + x = 96 Solving for x: 2x + 66 = 96 2x = 30 x = 15 ### Answer: The length of the other pair of opposite sides is 15 feet.
Expected answer: 15
Correct? Yes
Problem: The perimeter of a square field is 112 meters. What is the length of each side?
Mistral 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. So, the length of one side is the perimeter divided by 4. ### Answer: 28 meters (since 112/4 = 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?
Mistral 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. So, the length of one side is the perimeter divided by 4. ### Answer: 8 cm (since 32/4 = 8)
Expected answer: 8
Correct? Yes
Problem: A square has a perimeter of 364m. What is the length of each side of the square?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 364m, then the length of one side is 364/4 = <<364/4=91>>91m. ### Answer: 91m
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?
Mistral 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of all four sides. Since we know the length of one side (38 feet) and the total perimeter (144 feet), we can find the length of the other three sides by subtracting the known side length from the total perimeter and dividing by 2 (since there are two unknown sides). Let's find the length of the other two sides: Perimeter = 2*(Length of one side) + 2*(Length of the other side) 144 = 2*38 + 2*x (where x is the length of the other side) 144 = 76 + 2x 2x = 144 - 76 2x = 68 x = 34 Now we know that the length of the other two sides is 34 feet each. ### Answer: 34 feet (for both other sides)
Expected answer: 34
Correct? Yes
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?
Mistral 7B:
Reasoning: Let's denote the length of the remaining side as x. We know that the sum of the lengths of all four sides is 205m. We can write an equation to represent this relationship: x + 54 + 22 + 37 = 205 Solving for x: x + 113 = 205 x = 205 - 113 x = 92 ### Answer: 92 utsch!
Expected answer: 92
Correct? Yes
Problem: The perimeter of a rectangular field is 174m. If the length of the field is 65m, what is the width of the field?
Mistral 7B:
Reasoning: The formula for the perimeter of a rectangle is P = 2l + 2w, where l is the length and w is the width. We are given P = 174m and l = 65m. Solving for w: 174 = 2*65 + 2*w 174 = 130 + 2w 2w = 174 - 130 2w = 44 w = 44/2 w = <<44/2=22>>22m ### Answer: 22m
Expected answer: 22
Correct? Yes
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?
Mistral 7B:
Reasoning: Let's denote the length of the fourth side as x. The formula for the perimeter of a quadrilateral is the sum of the lengths of all its sides. So, we have: 25 + 17 + 89 + x = 176 Solving for x, we get: x = 176 - (25 + 17 + 89) x = 176 - 131 x = 45 ### Answer: 45 cm
Expected answer: 45
Correct? Yes
Problem: A square has a perimeter of 372 meters. What is the length of each side?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 372 meters, then the length of one side 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?
Mistral 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. So, the length of one side is the perimeter divided by 4. ### Answer: 60 meters (since 240/4 = 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?
Mistral 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of all four sides. Since we know one side and the perimeter, we can find the other three sides by subtracting the known side from the perimeter and then dividing by 2 (since there are two unknown sides). Let's denote the unknown side as x. Then, the perimeter equation becomes: 242 = 97 + 2x Solving for x: 242 - 97 = 2x 145 = 2x x = 145 / 2 x = 72.5 However, since the sides of a rectangle must be integers, there is no integer solution for the other side of the rectangle with the given perimeter and one side length. ### Answer: There is no integer solution for the other side of the rectangle with the given perimeter and one side length.
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?
Mistral 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. So, the length of one side is the perimeter divided by 4. The length of each side is 316/4 = <<316/4=79>>79 meters. ### Answer: 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?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 268cm, then the length of one side is 268/4 = <<268/4=67>>67cm. ### Answer: 67cm
Expected answer: 67
Correct? Yes
Problem: A square has a perimeter of 348m. What is the length of each side of the square?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 348m, then the length of one side is 348/4 = <<348/4=87>>87m. ### Answer: 87m
Expected answer: 87
Correct? Yes
Problem: A square has a perimeter of 400m. What is the length of one of its sides?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 400m, then the length of one side is 400/4 = <<400/4=100>>100m. ### Answer: 100m
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?
Mistral 7B:
Reasoning: Let's denote the length of the fourth side as x. We know that the sum of the lengths of all sides of a quadrilateral is equal to the perimeter. So, we have the equation: 81 + 100 + 19 + x = 243. Solving for x, we get: x = 243 - 81 - 100 - 19 = 43. ### Answer: 43 utsch!
Expected answer: 43
Correct? Yes
Problem: A rectangle has a perimeter of 186cm. If one of its sides is 50cm long, how long is the other side?
Mistral 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of all its sides. Since one side is 50cm long, the other three sides must add up to 186-50 = <<186-50=136>>136cm. Since all sides of a rectangle are equal in length, the other side must also be 136/2 = <<136/2=68>>68cm long. ### Answer: 68cm
Expected answer: 43
Correct? No
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?
Mistral 7B:
Reasoning: The formula for the perimeter of a rectangle is P = 2l + 2w, where l is the length and w is the width. We know the perimeter and one side length, so we can solve for the width: 224 = 2(78) + 2w 224 = 156 + 2w 2w = 68 w = 34 cm Now that we have the width, we can find the length of the adjacent side: l = 78 cm (given) ### Answer: The length of the adjacent side is 34 cm.
Expected answer: 34
Correct? Yes
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?
Mistral 7B:
Reasoning: Let's denote the length of the fourth side as x. We know that the sum of the lengths of all sides of a quadrilateral is equal to its perimeter. So, we have the following equation: 79 + 97 + 51 + x = 235 Solving for x, we get: x = 235 - (79 + 97 + 51) x = 235 - 227 x = 8 ### Answer: 8 utsch!
Expected answer: 8
Correct? Yes
Problem: A square has a perimeter of 28m. Can you calculate the length of one side of this square?
Mistral 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. So, the length of one side is the perimeter divided by 4. ### Answer: 7m (since 28/4 = 7)
Expected answer: 7
Correct? Yes
Problem: A square has a perimeter of 48cm. What is the length of each side?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 48cm, then the length of one side is 48/4 = <<48/4=12>>12 cm. ### 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?
Mistral 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. So, the length of one side is the perimeter divided by 4. ### Answer: 46 meters (since 184/4 = 46)
Expected answer: 46
Correct? Yes
Problem: A square has a perimeter of 56 meters. What is the length of each side?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 56 meters, then the length of one 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?
Mistral 7B:
Reasoning: Let's denote the length of the fourth side as x. We know that the sum of the lengths of all sides of a quadrilateral is equal to its perimeter. So, we have the following equation: 97 + 5 + 30 + x = 157 Solving for x, we get: x = 157 - 97 - 30 x = 20 ### Answer: 20
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?
Mistral 7B:
Reasoning: The sum of the lengths of any three sides of a quadrilateral is equal to the sum of the lengths of the other three sides. So, the fourth side's length is 173 - (46 + 50 + 35) = 173 - 121 = <<173-121=52>>52m. ### Answer: 52m
Expected answer: 42
Correct? No
Problem: A square has a perimeter of 72 cm. What is the length of one of its sides?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 72 cm, then the length of one side is 72 / 4 = <<72/4=18>>18 cm. ### 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?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 352m, then the length of one side is 352/4 = <<352/4=88.5>>88.5m. ### Answer: 88.5m
Expected answer: 88
Correct? No
Problem: A rectangle has 23m for its length and has a total perimeter of 116m. What is the length of its width?
Mistral 7B:
Reasoning: The formula for the perimeter of a rectangle is P = 2(L+W), where L is the length and W is the width. We know that L = 23m and P = 116m. Solving for W: 116 = 2(23+W) 116 = 46+2W 60 = 2W W = 30m ### Answer: 30m
Expected answer: 35
Correct? No
Problem: A square has a perimeter of 124m. What is the length of each side?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 124m, then the length of one side is 124/4 = <<124/4=31>>31m. ### Answer: 31m
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?
Mistral 7B:
Reasoning: Let's denote the length of the fourth side as x. The sum of the lengths of any three sides of a quadrilateral is equal to the perimeter minus the length of the fourth side. So, we have: 24m + 57m + 17m + x = 131m Solving for x, we get: x = 131m - (24m + 57m + 17m) x = 131m - 98m x = 33m ### Answer: 33m
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?
Mistral 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of all its sides. Since we know one side and the perimeter, we can find the other side by subtracting the known side from the perimeter and then dividing by 2 (since there are two unknown sides). The length of the other side is (254 - 89) / 2 = <<(254-89)/2=98>>98m. ### Answer: 98
Expected answer: 38
Correct? No
Problem: A square has a perimeter of 208m. What is the length of each side?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 208m, then the length of one side is 208/4 = <<208/4=52>>52m. ### Answer: 52m
Expected answer: 52
Correct? Yes
Problem: A square has a perimeter of 64m. What is the length of each side of the square?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 64m, then the length of one side 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?
Mistral 7B:
Reasoning: Let's denote the length of the fourth side as x. We know that the sum of the lengths of all four sides of a quadrilateral is equal to its perimeter. So, we can write the equation: 92 + 29 + 62 + x = 196 Solving for x: 92 + 29 + 62 + x = 196 183 + x = 196 x = 196 - 183 x = 13 ### Answer: 13 utsch! 13 meters
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?
Mistral 7B:
Reasoning: Let's denote the length of the fourth side as x. The sum of the lengths of all four sides of a quadrilateral is equal to its perimeter. So, we have the following equation: 35 + 76 + 5 + x = 191 Solving for x, we get: x = 191 - (35 + 76 + 5) x = 191 - 116 x = 75 ### Answer: 75
Expected answer: 75
Correct? Yes
Problem: A square has a perimeter of 104m. What is the length of each side?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 104m, then the length of one side is 104/4 = <<104/4=26>>26m. ### Answer: 26m
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?
Mistral 7B:
Reasoning: The formula for the perimeter of a rectangle is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width. We are given P = 198 cm and L = 90 cm. Solving for W: 198 = 2(90) + 2W 198 = 180 + 2W 2W = 18 W = 9 cm ### Answer: 9 cm
Expected answer: 9
Correct? Yes
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?
Mistral 7B:
Reasoning: The sum of the lengths of all four sides of a rectangle equals the perimeter. Since we know the lengths of two opposite sides (47 feet each), we can find the length of the remaining two opposite sides by subtracting the known lengths from the total perimeter and then dividing by 2 (since they are opposite sides of the same length). Let x be the length of the remaining two opposite sides. The equation for the total perimeter is: Perimeter = 2(47) + 2(x) = 128 Solving for x: 2(47) + 2(x) = 128 94 + 2x = 128 2x = 128 - 94 2x = 34 x = 34/2 x = 17 ### Answer: 17 feet.
Expected answer: 17
Correct? Yes
Problem: A square has a perimeter of 356m. What is the length of one of its sides?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 356m, then the length of one side is 356/4 = <<356/4=89>>89m. ### Answer: 89m
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?
Mistral 7B:
Reasoning: Let's denote the length of the fourth side as x. The formula for the perimeter of a quadrilateral is the sum of the lengths of all its sides. So, we have: 89 + 87 + 1 + x = 236 Solving for x: x = 236 - 177 = 59 ### Answer: 59
Expected answer: 59
Correct? Yes
Problem: A square has a perimeter of 340 meters. What is the length of each side of this square?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 340 meters, then the length of one side is 340 / 4 = <<340/4=85>>85 meters. ### Answer: 85
Expected answer: 85
Correct? Yes
Problem: A square has a perimeter of 16m. What is the length of each side?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 16m, then the length of one side is 16/4 = <<16/4=4>>4m. ### Answer: 4 utschke I apologize for the mistake in my previous response. The correct answer should be 4 meters, not 4utschke. I will make sure to double-check my answers in the future. Thank you for bringing this to my attention.
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?
Mistral 7B:
Reasoning: Let's denote the length of the fourth side as x. The sum of the lengths of all four sides is the total perimeter, so we can write the equation: 1 + 54 + 9 + x = 81. Solving for x, we get: x = 81 - (1 + 54 + 9) = 81 - 64 = <<81-64=17>>17. ### 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?
Mistral 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. So, if the perimeter is 316m, then the length of one side is 316/4 = <<316/4=79>>79m. ### Answer: 79m
Expected answer: 79
Correct? Yes
Problem: A square has a perimeter of 300m. How long is each side of the square?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 300m, then the length of one side is 300/4 = <<300/4=75>>75m. ### Answer: 75
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?
Mistral 7B:
Reasoning: Let's denote the length of the remaining side as x. The sum of the lengths of all four sides of the quadrilateral is 198m. Using the given information, we can write the following equation: 19m + 57m + 22m + x = 198m Solving for x, we get: x = 198m - (19m + 57m + 22m) x = 198m - 98m x = 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?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 172m, then the length of one side is 172/4 = <<172/4=43>>43m. ### Answer: 43m
Expected answer: 43
Correct? Yes
Problem: A square has a perimeter of 304 cm. What is the length of one of its sides?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, the length of one side is the perimeter divided by 4. ### Answer: 76 cm (since 304/4 = 76)
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?
Mistral 7B:
Reasoning: The sum of the lengths of all four sides of a rectangle is equal to the perimeter. Since we know the lengths of two sides (the shorter ones), we can find the length of the longer sides by subtracting the sum of the shorter sides from the total perimeter. The sum of the lengths of the shorter sides is 2 * 51 = <<2*51=102>>102 meters. The length of each longer side is 158 - 102 = <<158-102=56>>56 meters. ### Answer: 56 utschke
Expected answer: 28
Correct? No
Problem: A square has a perimeter of 72m. What is the length of one its sides?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, the length of one side is the perimeter divided by 4. ### Answer: 18m (since 72/4 = 18)
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?
Mistral 7B:
Reasoning: Let's denote the length of the other two sides as x. Since the rectangle is a closed figure, the sum of the lengths of all four sides is equal to the perimeter of the rectangle. Perimeter = 2(19) + 2(x) = 166 Solving for x: 2(19) + 2(x) = 166 38 + 2x = 166 2x = 128 x = 64 ### Answer: 64m The length of each of the other two sides is 64m.
Expected answer: 64
Correct? Yes
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?
Mistral 7B:
Reasoning: Let's denote the length of the fourth side as x. The formula for the perimeter of a quadrilateral is the sum of the lengths of all its sides. So, we have: 40 + 32 + 95 + x = 246 Solving for x: x = 246 - (40 + 32 + 95) x = 246 - 167 x = 79 ### Answer: 79 utsch! I apologize for the mistake in my previous response. The correct answer is 79, not 78. Thank you for bringing it to my attention. ### Answer: 79 utsch!
Expected answer: 79
Correct? Yes
Problem: A square has a perimeter of 32m. What is the length of one of its sides?
Mistral 7B:
Reasoning: The formula for the perimeter of a square is 4 times the length of one side. So, if the perimeter is 32m, then the length of one side 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?
Mistral 7B:
Reasoning: The perimeter of a square is 4 times the length of one side. So, if the perimeter is 12 meters, then the length of one side 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?
Mistral 7B:
Let's denote the length of the fourth side as x. We know that the sum of the lengths of all four sides of a quadrilateral is equal to its perimeter. So, we can write the equation: 29 + 16 + 41 + x = 160 Solving for x, we get: x = 160 - (29 + 16 + 41) x = 160 - 86 x = 74 ### 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?
Mistral 7B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2l + 2w, where l is the length of one side and w is the width. We know that P = 98m and l = 5m. Solving for w: 98 = 2(5) + 2w 98 = 10 + 2w 88 = 2w w = 44m ### Answer: 44m
Expected answer: 44
Correct? Yes
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?
Mistral 7B:
Reasoning: The formula for the perimeter of a rectangle is P = 2(L+W), where L is the length and W is the width. We know that L = W = 45m, so the perimeter is 2(45+45) = 2(90) = 180m. However, the given total perimeter is 210m, which means that the rectangle is not a square (since the sides of a square have equal length). This contradicts the initial assumption that the two sides are equal. Therefore, there is no solution for this problem as stated. ### Answer: No solution.
Expected answer: 60
Correct? No