Gemma 2B on 3.MD.D.8-quadrilateral
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?
Gemma 2B:
Reasoning: The perimeter of a rectangular swimming pool is given by the formula P = 2(length + width). Substituting the values, we get 324 = 2(83 + width). Solving for width, we get width = (324/2 - 83) = 108 meters. ### Answer: 108
Expected answer: 79
Correct? No
Problem: A square has a perimeter of 40m. What is the length of each side?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 40 = 4s. Solving for s, we get s = 10. ### 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?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 344 = 4s. Solving for s, we get s = 344/4 = <<86>>86. ### 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?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 348 = 4s. Solving for s, we get s = 348/4 = <<86>>86. ### Answer: 86
Expected answer: 87
Correct? No
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by P = 2(length + width). Substituting the values, we get 194 = 2(49 + width). Solving for width, we get width = (194 ÷ 2 - 49) = 53 cm. Therefore, the length of the other side is 49 cm.
Expected answer: 48
Correct? No
Problem: A square has a perimeter of 192m. What is the length of one side?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the length of one side. Substituting the values, we get 192 = 4s. Solving for s, we get s = 48. ### Answer: 48
Expected answer: 48
Correct? Yes
Problem: A square has a perimeter of 68cm. What is the length of one side?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the length of one side. Substituting the values, we get 68 = 4s. Solving for s, we get s = 17 cm. ### 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by P = 2(length + width). Substituting the values, we get 52 = 2(4 + width). Solving for width, we get width = (52 ÷ 2 - 4) = 12. Therefore, the other side measures 12 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is equal to the sum of the lengths of all four sides. Therefore, 229 = 93 + 98 + 36. The length of the fourth side is 229 - 93 - 98 = 24. ### Answer: 24
Expected answer: 2
Correct? No
Problem: The perimeter of a square is 16m. What is the length of each side of this square?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 16 = 4s. Solving for s, we get s = 4. ### Answer: 4m
Expected answer: 4
Correct? Yes
Problem: A square has a perimeter of 272m. What is the length of each side of the square?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 272 = 4s. Solving for s, we get s = 272/4 = <<68>>68. ### 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?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 244 = 4s. Solving for s, we get s = 61. ### 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = (a + b + c + d), where a, b, c, and d are the lengths of the four sides. Substituting the values, we get 227 = (70 + 29 + 61). Therefore, the length of the fourth side is 227 - 70 - 29 = 148m.
Expected answer: 67
Correct? No
Problem: A square has a perimeter of 280m. What is the length of the side of that square?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 280 = 4s. Solving for s, we get s = 70. ### Answer: 70
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = (a + b + c), where a, b, and c are the lengths of the three sides. Substituting the values, we get 219 = (37 + 98 + x), where x is the length of the fourth side. Solving for x, we get x = 219 - 37 - 98 = 74cm. ### Answer: 74
Expected answer: 43
Correct? No
Problem: A square has a perimeter of 44m. Can you calculate the length of one side?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the length of one side. Substituting the values, we get 44 = 4s. Solving for s, we get s = 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = (length + width). We are given that P = 282 and l = 71. Substituting these values into the formula, we get 282 = (71 + width). Solving for width, we get width = 282 - 71 = <<282-71=211>>211. Therefore, the length of the shorter side is 71 meters.
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get 128 = 2(57 + width). Solving for width, we get width = (128/2 - 57) = 34 meters. Therefore, the other side of the garden is 57 meters.
Expected answer: 7
Correct? No
Problem: A square has a perimeter of 392m. What is the length of each side of the square?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 392 = 4s. Solving for s, we get s = <<392/4=98>>98. ### 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by P = 2(length + width). Substituting the values, we get 204 = 2(16 + width). Solving for width, we get width = (204 ÷ 2 - 16) = 64. Therefore, the length of the other side is 16m.
Expected answer: 86
Correct? No
Problem: A square has a perimeter of 336cm. What is the length of one of its sides?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the length of one side. Substituting the values, we get 336 = 4s. Solving for s, we get s = 336/4 = 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?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the length of one side of the square. Substituting the values, we get 144 = 4s. Solving for s, we get s = 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = (a + b + c), where a, b, and c are the lengths of the three sides. Substituting the values, we get 236 = 69 + 50 + 39. Therefore, the length of the fourth side is 39 cm.
Expected answer: 78
Correct? No
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = (a + b + c + d), where a, b, c, and d are the lengths of the four sides. Substituting the values, we get 193 = (37 + 14 + 73 + x), where x is the length of the unknown side. Solving for x, we get x = 193 - 37 - 14 - 73 = 100cm. ### Answer: 100
Expected answer: 69
Correct? No
Problem: A square has a perimeter of 160m. What is the length of one of its sides?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the length of one side. Substituting the values, we get 160 = 4s. Solving for s, we get s = 40. ### Answer: 40
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get 228 = 2(90 + width). Solving for width, we get width = (228 ÷ 2 - 90) = 44 - 90 = 36 meters. ### Answer: 36
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?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 136 = 4s. Dividing both sides by 4, we get s = 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get 236 = 2(43 + width). Solving for width, we get width = (236 ÷ 2 - 43) = 69. Therefore, the length of the opposite side is 43 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?
Gemma 2B:
Reasoning: The perimeter is made up of four sides, each with a length of 58m. Two of these sides are equal, and the other two sides are equal. The missing portion is 1m. ### Answer: 1m
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?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 284 = 4s. Solving for s, we get s = 71. Therefore, each side of the square field is 71 meters long.
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get 150 = 2(69 + width). Solving for width, we get width = (150/2 - 69) = 41 feet. ### Answer: 41
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by P = 2(length + width). Substituting the values, we get 166 = 2(35 + width). Solving for width, we get width = (166/2 - 35) = 45. Therefore, the other side measures 45m.
Expected answer: 48
Correct? No
Problem: A square has a perimeter of 124m. What is the length of each side?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 124 = 4s. Solving for s, we get s = 31. ### Answer: 31
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values of the perimeter and one side length into the formula, we get 336 = 2(79 + width). Solving for width, we get width = (336 ÷ 2 - 79) = 133 feet. The length of the opposite side is 79 feet.
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?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the length of one side of the square. Substituting the values, we get 132 = 4s. Solving for s, we get s = 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get 138 = 2(46 + width). Solving for width, we get width = (138 ÷ 2 - 46) = 46. ### Answer: 46
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get 200 = 2(49 + width). Solving for width, we get width = (200/2 - 49) = 61 meters. ### Answer: 61
Expected answer: 51
Correct? No
Problem: A square has a perimeter of 200m. What is the length of each side?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 200 = 4s. Solving for s, we get s = 50. ### Answer: 50
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = (a + b + c + d), where a, b, c, and d are the lengths of the four sides. Substituting the values, we get 199 = (9 + 30 + 71). Therefore, the length of the fourth side is 9m.
Expected answer: 89
Correct? No
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = (a + b + c), where a, b and c are the lengths of the three sides. Substituting the values, we get 207 = (35 + 62 + 70). Therefore, the length of the fourth side is 207 - 35 - 62 = 110m.
Expected answer: 40
Correct? No
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by P = 2(length + width). Substituting the values, we get 384 = 2(99 + x), where x is the length of the longer side. Solving for x, we get x = (384/2 - 99)/2 = 192. ### Answer: 192
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = (a + b + c), where a, b, and c are the lengths of the three sides. Substituting the values, we get 255 = 78 + 15 + x, where x is the length of the fourth side. Solving for x, we get x = 255 - 78 - 15 = 162. ### Answer: 162
Expected answer: 99
Correct? No
Problem: A square has a perimeter of 128m. What is the length of one of its sides?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the length of one side. Substituting the values, we get 128 = 4s. Solving for s, we get s = 32. ### 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?
Gemma 2B:
Reasoning: The perimeter is the sum of the lengths of all sides. So, 96 = 33 + 33. ### Answer: 33
Expected answer: 15
Correct? No
Problem: The perimeter of a square field is 112 meters. What is the length of each side?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the length of each side. Substituting the values, we get 112 = 4s. Solving for s, we get s = 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?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the length of one side. Substituting the values, we get 32 = 4s. Solving for s, we get s = 8 cm. ### Answer: 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?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 364 = 4s. Solving for s, we get s = 91. ### 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get 144 = 2(38 + width). Solving for width, we get width = (144/2 - 38) = 48 feet. ### Answer: 48
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?
Gemma 2B:
Reasoning: Let x be the length of the remaining side. Then the other two sides are 54-x and 22-x. The perimeter is 205, so we have: x + (54-x) + (22-x) = 205 x + 54 - x - 22 = 205 32 = 205 x = 6.4m ### Answer: 6.4m
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?
Gemma 2B:
Reasoning: The perimeter of a rectangular field is given by the formula P = 2(length + width). Substituting the values, we get 174 = 2(65 + width). Solving for width, we get width = (174/2 - 65) = 55m.
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = (a + b + c), where a, b and c are the lengths of the three sides. Substituting the values, we get 176 = (25 + 17 + 89). Therefore, the length of the fourth side is 89 cm.
Expected answer: 45
Correct? No
Problem: A square has a perimeter of 372 meters. What is the length of each side?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 372 = 4s. Solving for s, we get s = <<372 ÷ 4>> = 93.5. ### Answer: 93.5
Expected answer: 93
Correct? No
Problem: A square field has a perimeter of 240 meters. Can you find out the length of one side of the field?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the length of one side of the square. Substituting the values, we get 240 = 4s. Dividing both sides by 4, we get s = 60. ### 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). We are given that P = 242 and one side = 97. Substituting these values into the formula, we get 242 = 2(97 + width). Solving for width, we get width = (242 ÷ 2 - 97) = 43. ### Answer: 43
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?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 316 = 4s. Solving for s, we get s = 316/4 = <<79>>79 meters. ### Answer: 79
Expected answer: 79
Correct? Yes
Problem: A square has a perimeter of 268cm. What is the length of each side of the square?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 268 = 4s. Solving for s, we get s = 268/4 = <<66>>66 cm. ### Answer: 66
Expected answer: 67
Correct? No
Problem: A square has a perimeter of 348m. What is the length of each side of the square?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 348 = 4s. Solving for s, we get s = 348/4 = <<86>>86. ### Answer: 86
Expected answer: 87
Correct? No
Problem: A square has a perimeter of 400m. What is the length of one of its sides?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the length of one side. Substituting the values, we get 400 = 4s. Solving for s, we get s = 100. ### 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = (a + b + c + d), where a, b, c, and d are the lengths of the four sides. Substituting the values, we get 243 = (81 + 100 + 19 + x), where x is the length of the fourth side. Solving for x, we get x = 243 - 81 - 100 - 19 = 144. ### Answer: 144
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by P = 2(length + width). Substituting the values, we get 186 = 2(50 + width). Solving for width, we get width = (186 ÷ 2 - 50) = 43cm. Therefore, the other side is 50cm.
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by P = 2(length + width). Substituting the values, we get 224 = 2(78 + width). Solving for width, we get width = (224 ÷ 2 - 78) = 48 cm. Therefore, the length of the adjacent side is 78 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(a + b), where a and b are the lengths of the two sides. Substituting the values, we get 2(79 + 97) = 2(176) = 352. The length of the fourth side is 51m.
Expected answer: 8
Correct? No
Problem: A square has a perimeter of 28m. Can you calculate the length of one side of this square?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the length of one side. Substituting the values, we get 28 = 4s. Solving for s, we get s = 7m. ### Answer: 7m
Expected answer: 7
Correct? Yes
Problem: A square has a perimeter of 48cm. What is the length of each side?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 48 = 4s. Solving for s, we get s = 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?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the length of one side. Substituting the values, we get 184 = 4s. Solving for s, we get s = 48. ### Answer: 48
Expected answer: 46
Correct? No
Problem: A square has a perimeter of 56 meters. What is the length of each side?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 56 = 4s. Solving for s, we get s = 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get 157 = 2(97 + 5 + 30). Solving for the fourth side length, we get 4 = 2(97 + 5 + 30). Therefore, the length of the fourth side is 2(97 + 5 + 30) = 2(132) = 264. ### Answer: 264
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = (a + b + c), where a, b and c are the lengths of the three sides. Substituting the values, we get 173 = 46 + 50 + 35. Therefore, the length of the fourth side is 46m.
Expected answer: 42
Correct? No
Problem: A square has a perimeter of 72 cm. What is the length of one of its sides?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the length of one side. Substituting the values, we get 72 = 4s. Solving for s, we get s = 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?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 352 = 4s. Solving for s, we get s = 352/4 = <<88>>88. ### Answer: 88
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get 116 = 2(23 + width). Solving for width, we get width = (116/2 - 23) = 34m.
Expected answer: 35
Correct? No
Problem: A square has a perimeter of 124m. What is the length of each side?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 124 = 4s. Solving for s, we get s = 31. ### 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is equal to the sum of the lengths of its four sides. Therefore, 24+57+17 = 131. The length of the fourth side is 17m.
Expected answer: 33
Correct? No
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by P = 2(length + width). Substituting the values, we get 254 = 2(89 + width). Solving for width, we get width = (254/2 - 89)/2 = 42. Therefore, the length of the other side is 89m.
Expected answer: 38
Correct? No
Problem: A square has a perimeter of 208m. What is the length of each side?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 208 = 4s. Solving for s, we get s = 52. ### 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?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 64 = 4s. Solving for s, we get s = 16. ### 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(a + b), where a and b are the lengths of the two sides. Substituting the values, we get 196 = 2(92 + 29 + x), where x is the length of the fourth side. Solving for x, we get x = 196 - 182 = 14. ### Answer: 14
Expected answer: 13
Correct? No
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?
Gemma 2B:
Reasoning: The perimeter is given by P = a + b + c + d, where a, b, c, and d are the lengths of the four sides. Substituting the values, we get 191 = 35 + 76 + 5 + d. Solving for d, we get d = 191 - 35 - 76 + 5 = 141. ### Answer: 141
Expected answer: 75
Correct? No
Problem: A square has a perimeter of 104m. What is the length of each side?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 104 = 4s. Solving for s, we get s = 26. ### 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get 198 = 2(90 + width). Solving for width, we get width = (198 ÷ 2 - 90) = 49 cm.
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get 128 = 2(47 + width). Solving for width, we get width = (128/2 - 47) = 31 feet. Therefore, the length of the remaining two opposite sides is 47 feet. ### Answer: 47
Expected answer: 17
Correct? No
Problem: A square has a perimeter of 356m. What is the length of one of its sides?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the length of one side. Substituting the values, we get 356 = 4s. Solving for s, we get s = 356/4 = <<86.5>>86.5. ### Answer: 86.5
Expected answer: 89
Correct? No
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is equal to the sum of the lengths of all its sides. Therefore, 236 = 89 + 87 + 1. Solving for the fourth side, we get 1 = 188 units. ### Answer: 188
Expected answer: 59
Correct? No
Problem: A square has a perimeter of 340 meters. What is the length of each side of this square?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 340 = 4s. Solving for s, we get s = 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?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 16 = 4s. Solving for s, we get s = 4. ### Answer: 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values of the sides, we get 81 = 2(1 + 54). Solving for the fourth side, we get 4 = 2(54). Therefore, the length of the fourth side is 2(54) = 108m.
Expected answer: 17
Correct? No
Problem: A quadrilateral, which is a perfect square, has a total perimeter of 316m. What is the length of each side of this square?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 316 = 4s. Solving for s, we get s = 316/4 = <<79>>79. ### Answer: 79
Expected answer: 79
Correct? Yes
Problem: A square has a perimeter of 300m. How long is each side of the square?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 300 = 4s. Solving for s, we get s = 75. ### 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = (a + b + c), where a, b, and c are the lengths of the three sides. Substituting the values, we get 198 = (19 + 57 + 22). Therefore, the length of the remaining side is 22m.
Expected answer: 100
Correct? No
Problem: A square has a perimeter of 172m. What is the length of each side of the square?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 172 = 4s. Solving for s, we get s = 48. ### Answer: 48
Expected answer: 43
Correct? No
Problem: A square has a perimeter of 304 cm. What is the length of one of its sides?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the length of one side. Substituting the values, we get 304 = 4s. Solving for s, we get s = 76 cm. ### Answer: 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by P = 2(length + width). Substituting the values, we get 158 = 2(51 + width). Solving for width, we get width = (158 ÷ 2 - 51) = 49. Therefore, the length of each longer side is 51 meters.
Expected answer: 28
Correct? No
Problem: A square has a perimeter of 72m. What is the length of one its sides?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get 72 = 4s. Solving for s, we get s = 18. ### Answer: 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?
Gemma 2B:
Reasoning: The total length of the fence is 166m, and two sides are 19m each. Therefore, the other two sides must be 166-19 = <<166-19=147>>147m long.
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is equal to the sum of the lengths of all its sides. Therefore, 2(40+32+95) = 240 + 88 + 95 = 246. The length of the fourth side is 95m.
Expected answer: 79
Correct? No
Problem: A square has a perimeter of 32m. What is the length of one of its sides?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the length of one side. Substituting the values, we get 32 = 4s. Solving for s, we get s = 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?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the length of one side of the square. Substituting the values, we get 12 = 4s. Solving for s, we get s = 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = (a + b + c), where a, b, and c are the lengths of the three sides. Substituting the values, we get 160 = (29 + 16 + 41). Therefore, the length of the fourth side is 41m.
Expected answer: 74
Correct? No
Problem: A rectangle has a perimeter of 98m. If one of its sides is 5m long, what is the length of the other side?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by P = 2(length + width). Substituting the values, we get 98 = 2(5 + width). Solving for width, we get width = (98/2 - 5) = 47. Therefore, the length of the other side is 5m.
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get 2(45) = 90. Therefore, the length of each of the other two sides is 45m.
Expected answer: 60
Correct? No