Common Core Standard 3.MD.D.8-polygon
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: A sum of several measurements taken along the edge of a plot of land totals to 368 miles. The individual measurements are 41 miles, 28 miles, 90 miles, 32 miles, 10 miles, and 98 miles. What is the remaining measurement that hasn't been included in the total yet?
GPT-3.5 Turbo:
Reasoning: The sum of the given measurements is 41 + 28 + 90 + 32 + 10 + 98 = 299 miles. The remaining measurement is 368 - 299 = <<368-299=69>>69 miles. ### Answer: 69
Expected answer: 69
Correct? Yes
Problem: A regular pentagon has side lengths of 70cm, 36cm, 53cm, and 45cm. If the total perimeter of the pentagon is 300cm, what is the length of its fifth side?
GPT-3.5 Turbo:
Let the length of the fifth side be \( x \) cm. The total perimeter of the pentagon is the sum of all five sides, so we have: \[ 70 + 36 + 53 + 45 + x = 300 \] Adding the given side lengths, we get: \[ 204 + x = 300 \] Subtracting 204 from both sides gives: \[ x = 300 - 204 = 96 \] Therefore, the length of the fifth side is 96 cm. ### Answer: 96 cm.
Expected answer: 96
Correct? Yes
Problem: A regular nonagon (9-sided polygon) has side lengths of 14cm, 94cm, 3cm, 20cm, 57cm, 83cm, 96cm, and 85cm. If the perimeter of the nonagon is 521cm, what is the length of the ninth side?
GPT-3.5 Turbo:
To find the length of the ninth side, we need to subtract the sum of the given side lengths from the total perimeter of the nonagon: 521 - (14 + 94 + 3 + 20 + 57 + 83 + 96 + 85) = 521 - 452 = 69. Therefore, the length of the ninth side is 69 cm. ### Answer: 69 cm.
Expected answer: 69
Correct? Yes
Problem: A polygon has sides measuring 54cm, 51cm, 5cm, 22cm, and 93cm. If the total perimeter of the polygon is 274cm, what is the length of the sixth side?
GPT-3.5 Turbo:
To find the length of the sixth side, we need to subtract the sum of the given sides from the total perimeter: Perimeter of the polygon = 54cm + 51cm + 5cm + 22cm + 93cm + x = 274cm, where x is the length of the sixth side. Solving for x: x = 274cm - (54cm + 51cm + 5cm + 22cm + 93cm) x = 274cm - 225cm x = 49cm ### Answer: 49cm.
Expected answer: 49
Correct? Yes
Problem: A regular pentagon has a perimeter of 310 m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: A regular pentagon has 5 equal sides. Therefore, the length of each side is the perimeter divided by 5: 310 m / 5 = <<310/5=62>>62 m. ### Answer: 62 m.
Expected answer: 62
Correct? Yes
Problem: A polygon has side lengths of 78cm, 93cm, 21cm, 4cm, and 21cm. If the total perimeter of the shape is 315cm, then what is the length of the last side?
GPT-3.5 Turbo:
To find the length of the last side, we need to subtract the sum of the given side lengths from the total perimeter: 315 - (78 + 93 + 21 + 4 + 21) = 315 - 217 = 98 cm. ### Answer: 98 cm.
Expected answer: 98
Correct? Yes
Problem: A regular 8-sided polygon, an octagon, has a perimeter of 160m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: Since an octagon has 8 sides, each side has the same length. Let x be the length of each side. The perimeter of the octagon is given by 8x = 160m. Solving for x, we have x = 160m / 8 = 20m. ### Answer: Each side of the octagon is 20 meters long.
Expected answer: 20
Correct? Yes
Problem: Consider an octagon. Its seven sides have lengths 6cm, 4cm, 95cm, 34cm, 19cm, 14cm, and 26cm. What is the length of the other side if the total perimeter of the octagon is 224cm?
GPT-3.5 Turbo:
Reasoning: The total perimeter of the octagon is the sum of the lengths of all its sides. Therefore, the length of the missing side is: 224 - (6 + 4 + 95 + 34 + 19 + 14 + 26) = 224 - 198 = 26 cm. ### Answer: 26 cm.
Expected answer: 26
Correct? Yes
Problem: A regular hexagon has a perimeter of 174 meters. If all sides are equal, what is the length of one side?
GPT-3.5 Turbo:
Reasoning: Since a regular hexagon has 6 equal sides, the length of one side is the perimeter divided by the number of sides, so each side is 174/6 = <<174/6=29>>29 meters long. ### Answer: 29 meters.
Expected answer: 29
Correct? Yes
Problem: A dodecagon has side lengths of 65cm, 22cm, 32cm, 31cm, 78cm, 88cm, 7cm, 29cm, 36cm, and 54cm. The total perimeter of the dodecagon is 538cm. What is the length of the 11th side?
GPT-3.5 Turbo:
To find the length of the 11th side, we need to subtract the sum of the lengths of the first 10 sides from the total perimeter of the dodecagon. Sum of the lengths of the first 10 sides: 65 + 22 + 32 + 31 + 78 + 88 + 7 + 29 + 36 + 54 = 442 Length of the 11th side: 538 - 442 = 96 ### Answer: 96 cm.
Expected answer: 96
Correct? Yes
Problem: A hexagon has five side lengths of 61 cm, 84 cm, 80 cm, 11 cm, and 71 cm. What should be the length of the last side so that the sum of lengths of all sides is 357 cm?
GPT-3.5 Turbo:
Reasoning: The sum of the lengths of all sides of the hexagon is 357 cm. Given that the lengths of five sides are 61 cm, 84 cm, 80 cm, 11 cm, and 71 cm, the sum of these lengths is 61+84+80+11+71 = 307 cm. Therefore, the length of the last side should be 357 - 307 = <<357-307=50>>50 cm. ### Answer: 50 cm.
Expected answer: 50
Correct? Yes
Problem: A regular octagon has a perimeter of 544m. What is the length of one side?
GPT-3.5 Turbo:
Reasoning: Since a regular octagon has 8 equal sides, we can divide the perimeter by 8 to find the length of one side. Each side of the octagon is 544m / 8 = <<544/8=68>>68m long. ### Answer: 68m.
Expected answer: 68
Correct? Yes
Problem: The perimeter of a regular decagon (10-sided polygon) is 960m. Find the length of one side.
GPT-3.5 Turbo:
Reasoning: Since a regular decagon has 10 sides, each side is equal in length. Let \( s \) be the length of one side. The perimeter of the decagon is given by \( \text{Perimeter} = 10s = 960 \). Solving for \( s \), we have \( s = \frac{960}{10} = 96 \) meters. ### Answer: 96 meters.
Expected answer: 96
Correct? Yes
Problem: A regular heptagon (7-sided polygon) has an unknown side length. If its total perimeter is 203m, how long is each side?
GPT-3.5 Turbo:
Reasoning: Since a regular heptagon has 7 sides, we can divide the total perimeter by 7 to find the length of each side. Each side length is 203m / 7 = <<203/7=29>>29m. ### Answer: 29m.
Expected answer: 29
Correct? Yes
Problem: A regular heptagon (7-sided polygon) has a perimeter of 49 meters. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: Since a regular heptagon has 7 sides, the length of each side is the total perimeter divided by the number of sides. Therefore, each side has a length of 49 meters / 7 sides = 7 meters. ### Answer: 7 meters.
Expected answer: 7
Correct? Yes
Problem: The perimeter of a regular heptagon is 329m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: A regular heptagon has 7 equal sides. Let the length of each side be \(x\). Therefore, the perimeter of the heptagon is \(7x\). Given that the perimeter is 329m, we have the equation \(7x = 329\). Solving for \(x\), we get \(x = \frac{329}{7} = 47\). ### Answer: The length of each side is 47m.
Expected answer: 47
Correct? Yes
Problem: The sides of a heptagon have lengths of 86m, 80m, 47m, 93m, and 99m. If the total perimeter of the heptagon is 486m, what is the length of the sixth side?
GPT-3.5 Turbo:
Reasoning: The total perimeter of the heptagon is the sum of all the side lengths. Let the length of the sixth side be x. Therefore, the total perimeter is 86 + 80 + 47 + 93 + 99 + x = 486. Solving for x, we get x = 486 - (86 + 80 + 47 + 93 + 99) = 486 - 405 = 81m. ### Answer: 81m.
Expected answer: 81
Correct? Yes
Problem: A regular heptagon has a perimeter of 546m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: A regular heptagon has 7 sides, so the length of each side is the perimeter divided by the number of sides: 546m / 7 = <<546/7=78>>78m. ### Answer: 78m
Expected answer: 78
Correct? Yes
Problem: A nonagon (nine-sided polygon) has 8 of its sides with lengths 26cm, 45cm, 75cm, 68cm, 63cm, 80cm, and 100cm, respectively. If the perimeter of the nonagon is 532cm, what is the length of the ninth side?
GPT-3.5 Turbo:
Reasoning: The perimeter of the nonagon is the sum of the lengths of all its sides. So, the sum of the lengths of the given 8 sides is 26+45+75+68+63+80+100 = 457 cm. Therefore, the length of the ninth side is 532 - 457 = 75 cm. ### Answer: 75 cm.
Expected answer: 75
Correct? Yes
Problem: The sides of a decagon are 62m, 76m, 98m, 74m, another unknown side, 54m, 4m, 24m, and 48m respectively. All sides are equal in length. If the perimeter of the shape is 452m, what is the length of the unknown side?
GPT-3.5 Turbo:
Reasoning: A decagon has 10 sides, so the sum of all the sides is 452m. We can find the sum of the given sides: 62 + 76 + 98 + 74 + 54 + 4 + 24 + 48 = 440m. To find the length of the unknown side, we subtract the sum of the given sides from the total perimeter: 452 - 440 = 12m. ### Answer: 12m.
Expected answer: 12
Correct? Yes
Problem: A regular hexagon has a perimeter of 78m. What is the length of each side?
GPT-3.5 Turbo:
Given that a regular hexagon has 6 equal sides, we can divide the perimeter by 6 to find the length of each side. Each side length = 78m / 6 = <<78/6=13>>13m. ### Answer: 13m.
Expected answer: 13
Correct? Yes
Problem: A regular nonagon has a perimeter of 171m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: A regular nonagon has 9 sides, so the length of each side is the perimeter divided by the number of sides: 171m / 9 = <<171/9=19>>19m. ### Answer: 19m.
Expected answer: 19
Correct? Yes
Problem: A nonagon has the following side lengths: 8 cm, 17 cm, 30 cm, 17 cm, 86 cm, 55cm, and 68cm. It also has one unknown side length. The overall perimeter of the nonagon is 318 cm. What is the length of the unknown side?
GPT-3.5 Turbo:
To find the length of the unknown side, we first need to sum up all the given side lengths: 8 + 17 + 30 + 17 + 86 + 55 + 68 = 281 cm. Let the length of the unknown side be x. The overall perimeter is the sum of all side lengths, so we have: 281 + x = 318. Solving for x: x = 318 - 281, x = 37. Therefore, the length of the unknown side is 37 cm. ### Answer: 37 cm.
Expected answer: 37
Correct? Yes
Problem: An 11-sided regular polygon has a perimeter of 858m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: The sum of the lengths of all sides of a polygon is equal to its perimeter. Since the polygon is regular, all sides have the same length. Let \( s \) be the length of each side. The perimeter of the polygon is given as 858m. Since the polygon has 11 sides, we have: \[ 11s = 858 \] Solving for \( s \): \[ s = \frac{858}{11} = 78 \] Therefore, the length of each side is 78m. ### Answer: 78m
Expected answer: 78
Correct? Yes
Problem: A regular decagon has a perimeter of 360m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: A regular decagon has 10 sides, so each side has a length of 360m / 10 = <<360/10=36>>36m. ### Answer: 36m.
Expected answer: 36
Correct? Yes
Problem: A regular hexagon has a perimeter of 522m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: A regular hexagon has 6 equal sides. Therefore, the length of each side is the perimeter divided by the number of sides, which is 522m / 6 = <<522/6=87>>87m. ### Answer: 87m
Expected answer: 87
Correct? Yes
Problem: A regular polygon has a perimeter of 418m. If each side is the same length, what is the length of each side? Assume the polygon has 11 sides.
GPT-3.5 Turbo:
Reasoning: Since the polygon has 11 sides, the length of each side is 418m/11 = <<418/11=38>>38m. ### Answer: 38m
Expected answer: 38
Correct? Yes
Problem: A polygon has side lengths of 56m, 73m, 39m, 24m, and 26m. If the total perimeter of the polygon is 278m, what is the length of the sixth side?
GPT-3.5 Turbo:
Reasoning: The total perimeter of the polygon is the sum of all the side lengths. So, 56m + 73m + 39m + 24m + 26m + x = 278m, where x is the length of the sixth side. Combining like terms, we get 218m + x = 278m. Subtracting 218m from both sides, we get x = 60m. ### Answer: 60m.
Expected answer: 60
Correct? Yes
Problem: A regular pentagon has a perimeter of 385cm. How long is each side?
GPT-3.5 Turbo:
Reasoning: A regular pentagon has 5 equal sides. Therefore, the length of each side is the perimeter divided by 5: 385cm / 5 = <<385/5=77>>77cm. ### Answer: 77 cm.
Expected answer: 77
Correct? Yes
Problem: The perimeter of a very irregular eleven-sided polygon is 663m. Of those eleven sides, ten are known to be 97m, 93m, 35m, 1m, 27m, 86m, 68m, 96m, 45m, and 61m respectively. What is the length of the unknown eleventh side?
GPT-3.5 Turbo:
Reasoning: The perimeter of a polygon is the sum of the lengths of all its sides. Therefore, the sum of the lengths of the ten known sides is 97+93+35+1+27+86+68+96+45+61 = 609m. To find the length of the unknown eleventh side, we subtract the sum of the lengths of the known sides from the total perimeter: 663 - 609 = 54m. ### Answer: 54m.
Expected answer: 54
Correct? Yes
Problem: A decagon has side lengths of 54m, 49m, 85m, 48m, 85m, 19m, 94m, 44m, and 54m respectively. The length of the tenth side is not known. What is the length of this side if the total perimeter of the decagon is 575m?
GPT-3.5 Turbo:
Reasoning: The total perimeter of the decagon is the sum of all the side lengths. Let the length of the tenth side be x. So, the total perimeter is 54 + 49 + 85 + 48 + 85 + 19 + 94 + 44 + 54 + x = 575. Simplifying this equation gives x = 575 - (54 + 49 + 85 + 48 + 85 + 19 + 94 + 44 + 54) = 575 - 532 = 43m. ### Answer: 43m.
Expected answer: 43
Correct? Yes
Problem: Given a regular octagon with a perimeter of 248m, what is the length of each side?
GPT-3.5 Turbo:
Reasoning: Since a regular octagon has 8 equal sides, we can divide the perimeter by 8 to find the length of each side. Each side length is 248m / 8 = <<248/8=31>>31m. ### Answer: 31m.
Expected answer: 31
Correct? Yes
Problem: A regular pentagon has a perimeter of 390m. What is the length of each side?
GPT-3.5 Turbo:
A regular pentagon has 5 equal sides. Let x be the length of each side. The perimeter of a regular pentagon is given by P = 5x. Given that the perimeter is 390m, we have: 5x = 390 Dividing both sides by 5, we get: x = 390/5 x = 78 Therefore, the length of each side of the regular pentagon is 78m. ### Answer: 78m
Expected answer: 78
Correct? Yes
Problem: A decagon has nine side lengths given as 6m, 85m, 83m, 73m, 25m, 66m, 54m, 87m, and 21m. If the total perimeter is 522m, find the length of the tenth side.
GPT-3.5 Turbo:
Reasoning: The total perimeter of the decagon is the sum of all the side lengths, so we have: 6m + 85m + 83m + 73m + 25m + 66m + 54m + 87m + 21m + x = 522m, where x is the length of the tenth side. Adding all the given side lengths, we get: 6 + 85 + 83 + 73 + 25 + 66 + 54 + 87 + 21 = 410. Substitute this back into the first equation: 410 + x = 522, x = 522 - 410, x = 112. ### Answer: 112m.
Expected answer: 22
Correct? No
Problem: A regular octagon has a perimeter of 408m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: Since a regular octagon has 8 equal sides, we can divide the perimeter by 8 to find the length of each side. Each side length is 408m / 8 = <<408/8=51>>51m. ### Answer: 51m.
Expected answer: 51
Correct? Yes
Problem: An octagon has an equal length of sides. If the perimeter of the octagon is 696m, what is the length of each side?
GPT-3.5 Turbo:
Reasoning: Since an octagon has 8 equal sides, the length of each side can be found by dividing the perimeter by the number of sides. Therefore, the length of each side is 696m / 8 = <<696/8=87>>87m. ### Answer: 87m
Expected answer: 87
Correct? Yes
Problem: An octagon has a perimeter of 744m. What is the length of each side if all sides are equal?
GPT-3.5 Turbo:
Reasoning: An octagon has 8 sides, so if all sides are equal, each side has a length of 744m/8 = <<744/8=93>>93m. ### Answer: 93m
Expected answer: 93
Correct? Yes
Problem: A regular nonagon (9-sided polygon) has a perimeter of 270m. What is the length of one side?
GPT-3.5 Turbo:
Reasoning: Since a regular nonagon has 9 sides, the length of each side is the total perimeter divided by the number of sides. Therefore, the length of one side is 270m / 9 = <<270/9=30>>30m. ### Answer: 30m.
Expected answer: 30
Correct? Yes
Problem: A nonagon nine-sided polygon has eight known side lengths: 30cm, 18cm, 68cm, 23cm, 72cm, 57cm, 33cm, and 19cm. If the total perimeter of the nonagon is 350cm, what is the length of the unknown ninth side?
GPT-3.5 Turbo:
Reasoning: The total of the eight known side lengths is 30+18+68+23+72+57+33+19 = 320 cm. The length of the unknown ninth side is 350 - 320 = 30 cm. ### Answer: 30 cm.
Expected answer: 30
Correct? Yes
Problem: A nonagon has eight side lengths known which are 19m, 7m, 10m, 16m, 32m, 15m and 70m. What is the length of the ninth side if the total perimeter of the nonagon is 188m?
GPT-3.5 Turbo:
Reasoning: The total perimeter of the nonagon is the sum of all nine side lengths. We know the lengths of eight sides are 19m, 7m, 10m, 16m, 32m, 15m, 70m, and the unknown ninth side length is x. Therefore, the total perimeter is 19 + 7 + 10 + 16 + 32 + 15 + 70 + x = 188. Solving for x, we get x = 188 - (19 + 7 + 10 + 16 + 32 + 15 + 70) = 188 - 169 = 19m. ### Answer: 19m.
Expected answer: 19
Correct? Yes
Problem: A regular hexagon has a perimeter of 90m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: A regular hexagon has 6 equal sides. Therefore, the length of each side is the perimeter divided by the number of sides, which is 90m/6 = <<90/6=15>>15m. ### Answer: 15m
Expected answer: 15
Correct? Yes
Problem: A regular heptagon (7-sided polygon) has a perimeter of 287m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: Since a regular heptagon has 7 sides, the length of each side can be found by dividing the perimeter by the number of sides. Therefore, the length of each side is 287m / 7 = <<287/7=41>>41m. ### Answer: 41m
Expected answer: 41
Correct? Yes
Problem: A regular pentagon has a perimeter of 50m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: A regular pentagon has 5 equal sides. Therefore, the length of each side is the perimeter divided by the number of sides, which is 50m/5 = <<50/5=10>>10m. ### Answer: 10m
Expected answer: 10
Correct? Yes
Problem: A regular nonagon has a perimeter of 63m. What is the length of each side?
GPT-3.5 Turbo:
A regular nonagon has 9 sides, so the length of each side is the perimeter divided by the number of sides: 63m / 9 = <<63/9=7>>7m. ### Answer: 7m
Expected answer: 7
Correct? Yes
Problem: A regular hexagon has a perimeter of 354m. What is the length of one side of this hexagon?
GPT-3.5 Turbo:
Given that a regular hexagon has 6 equal sides, we can find the length of one side by dividing the perimeter by the number of sides. Each side of the hexagon is 354m / 6 = <<354/6=59>>59m long. ### Answer: 59m
Expected answer: 59
Correct? Yes
Problem: A polygon has side lengths of 59m, 16m, 15m, 35m, 89m, 16m, 43m and 7m. If the total perimeter of the polygon is 286m, what is the length of the last unknown side?
GPT-3.5 Turbo:
To find the length of the last unknown side, we need to subtract the sum of the given side lengths from the total perimeter of the polygon. Sum of the given side lengths = 59 + 16 + 15 + 35 + 89 + 16 + 43 + 7 = 280m Length of the last unknown side = Total perimeter - Sum of given side lengths Length of the last unknown side = 286 - 280 = 6m ### Answer: 6m
Expected answer: 6
Correct? Yes
Problem: A regular heptagon (7-sided polygon) has a perimeter of 616m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: Since a regular heptagon has 7 sides, the length of each side is the total perimeter divided by 7. Therefore, each side has a length of 616m / 7 = <<616/7=88>>88m. ### Answer: 88m
Expected answer: 88
Correct? Yes
Problem: A regular hexagon has a perimeter of 36m. What is the length of each side?
GPT-3.5 Turbo:
Given that a regular hexagon has 6 equal sides, we can divide the perimeter by the number of sides to find the length of each side. Each side length is 36m / 6 = <<36/6=6>>6m. ### Answer: 6m.
Expected answer: 6
Correct? Yes
Problem: A dodecagon has 11 of its 12 sides already measured. The lengths are 88cm, 24cm, 83cm, 64cm, 16cm, 14cm, 90cm, 36cm, and 47cm respectively. If the total perimeter of the dodecagon is 492cm, what is the length of the twelfth side?
GPT-3.5 Turbo:
Reasoning: The total perimeter of the dodecagon is the sum of all its side lengths. We can find the sum of the 9 measured sides: 88+24+83+64+16+14+90+36+47 = 462 cm. To find the length of the twelfth side, we subtract the sum of the 9 measured sides from the total perimeter: 492 - 462 = 30 cm. ### Answer: 30 cm.
Expected answer: 30
Correct? Yes
Problem: A regular hexagon has a perimeter of 306m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: A regular hexagon has 6 equal sides. Therefore, the length of each side is the perimeter divided by the number of sides, which is 306m / 6 = <<306/6=51>>51m. ### Answer: 51m
Expected answer: 51
Correct? Yes
Problem: A regular heptagon (7-sided polygon) has a perimeter of 238 meters. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: Since a regular heptagon has 7 sides, the length of each side is the total perimeter divided by the number of sides. Therefore, each side has a length of 238/7 = <<238/7=34>>34 meters. ### Answer: 34 meters.
Expected answer: 34
Correct? Yes
Problem: A regular hexagon has a total perimeter of 42m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: A regular hexagon has 6 equal sides. Therefore, each side of the hexagon is 42m / 6 = <<42/6=7>>7m. ### Answer: 7m
Expected answer: 7
Correct? Yes
Problem: A regular octagon has a perimeter of 624m. What is the length of each side of the octagon?
GPT-3.5 Turbo:
Reasoning: Since a regular octagon has 8 equal sides, we can divide the perimeter by 8 to find the length of each side. Each side of the octagon is 624m / 8 = <<624/8=78>>78m. ### Answer: 78m
Expected answer: 78
Correct? Yes
Problem: A polygon with nine sides has lengths of 17m, 13m, 61m, 16m, 11m, 83m, 28m, 48m, and 93m. What is the length of the tenth side if the total perimeter of the polygon is 468 meters?
GPT-3.5 Turbo:
To find the length of the tenth side, we first need to find the sum of the lengths of the given sides: 17 + 13 + 61 + 16 + 11 + 83 + 28 + 48 + 93 = 370 meters. To find the length of the tenth side, we subtract the sum of the given sides from the total perimeter: 468 - 370 = 98 meters. Therefore, the length of the tenth side is 98 meters. ### Answer: 98 meters.
Expected answer: 98
Correct? Yes
Problem: A regular pentagon has a perimeter of 380m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: A regular pentagon has 5 equal sides. Therefore, the length of each side is the perimeter divided by 5: 380m / 5 = <<380/5=76>>76m. ### Answer: 76m
Expected answer: 76
Correct? Yes
Problem: A regular octagon has a perimeter of 104cm. What is the length of one of its sides?
GPT-3.5 Turbo:
Reasoning: Since a regular octagon has 8 equal sides, the length of one side is the perimeter divided by 8. Therefore, the length of one side is 104/8 = <<104/8=13>>13 cm. ### Answer: 13 cm.
Expected answer: 13
Correct? Yes
Problem: A regular heptagon (7-sided polygon) has a perimeter of 637m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: Since a regular heptagon has 7 sides, the length of each side is the total perimeter divided by the number of sides. Therefore, the length of each side is 637m / 7 = <<637/7=91>>91m. ### Answer: 91m
Expected answer: 91
Correct? Yes
Problem: A regular pentagon has a perimeter of 35m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: A regular pentagon has 5 equal sides. Let the length of each side be \( s \) meters. Therefore, the perimeter of the pentagon is \( 5s = 35 \) meters. Solving for \( s \), we get \( s = \frac{35}{5} = 7 \) meters. ### Answer: 7 meters.
Expected answer: 7
Correct? Yes
Problem: The perimeter of a pentagon is 223cm. The lengths of four of its sides are 45cm, 93cm, 36cm, and 22cm respectively. What is the length of the fifth side?
GPT-3.5 Turbo:
Reasoning: The perimeter of a pentagon is the sum of the lengths of all its sides. Therefore, the length of the fifth side is: 223 - (45 + 93 + 36 + 22) = 27 cm. ### Answer: 27 cm.
Expected answer: 27
Correct? Yes
Problem: A polygon has sides measuring 75cm, 81cm, 22cm, 94cm, 91cm, and 10cm. If the perimeter of the polygon is 423cm, what is the length of the last unknown side?
GPT-3.5 Turbo:
To find the length of the last unknown side, we need to subtract the sum of the given sides from the total perimeter of the polygon. Given sides: 75cm + 81cm + 22cm + 94cm + 91cm + 10cm = 373cm Unknown side: 423cm - 373cm = 50cm Therefore, the length of the last unknown side is 50cm. ### Answer: 50cm.
Expected answer: 50
Correct? Yes
Problem: A regular decagon (10-sided polygon) has a perimeter of 600m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: Since a regular decagon has 10 sides, the length of each side is the total perimeter divided by the number of sides, so each side is 600m/10 = <<600/10=60>>60m long. ### Answer: 60m.
Expected answer: 60
Correct? Yes
Problem: The perimeter of a regular octagon is 632m. What is the length of each of its sides?
GPT-3.5 Turbo:
Reasoning: Since a regular octagon has 8 equal sides, we can divide the perimeter by 8 to find the length of each side. Each side length = 632m / 8 = <<632/8=79>>79m. ### Answer: 79m.
Expected answer: 79
Correct? Yes
Problem: A regular septagon (7-sided polygon) has a total perimeter of 161m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: Since a regular septagon has 7 sides, each side has the same length. Let x be the length of each side. The total perimeter is given by 7x = 161m. Solving for x, we have x = 161m / 7 = 23m. ### Answer: 23m.
Expected answer: 23
Correct? Yes
Problem: A regular hexagon has a perimeter of 96m. What is the length of each side?
GPT-3.5 Turbo:
A regular hexagon has 6 equal sides. Perimeter of a hexagon = 6 * length of each side Given perimeter = 96m So, 6 * length of each side = 96 Dividing both sides by 6, we get: Length of each side = 96 / 6 = 16m ### Answer: 16m
Expected answer: 16
Correct? Yes
Problem: A nonagon (9-sided polygon), has sides with length 50m, 31m, 24m, 28m, 13m, 97m, 63m and 88m. Find the length of the ninth side if the total perimeter of the nonagon is 402m.
GPT-3.5 Turbo:
To find the length of the ninth side, we need to subtract the sum of the given side lengths from the total perimeter of the nonagon. Given side lengths: 50m + 31m + 24m + 28m + 13m + 97m + 63m + 88m = 394m Length of the ninth side = Total perimeter - Sum of given side lengths Length of the ninth side = 402m - 394m = 8m ### Answer: 8m.
Expected answer: 8
Correct? Yes
Problem: A regular heptagon (7-sided polygon) has a perimeter of 385m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: Since a regular heptagon has 7 sides, the length of each side is the total perimeter divided by the number of sides. Therefore, the length of each side is 385m / 7 = <<385/7=55>>55m. ### Answer: 55m
Expected answer: 55
Correct? Yes
Problem: The total perimeter of a polygon is 358 meters. The lengths of five of its sides are 89 meters, 2 meters, 10 meters, 48 meters, and 94 meters respectively, and another side measures 59 meters. What is the length of the remaining side?
GPT-3.5 Turbo:
Reasoning: The total perimeter of the polygon is the sum of the lengths of all its sides. We know the lengths of five sides are 89 + 2 + 10 + 48 + 94 = 243 meters. Therefore, the length of the remaining side is 358 - 243 = 115 meters. ### Answer: 115 meters.
Expected answer: 56
Correct? No
Problem: An octagon has a equal sides and its total perimeter is 496m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: An octagon has 8 equal sides, so each side has a length of 496m / 8 = <<496/8=62>>62m. ### Answer: 62m
Expected answer: 62
Correct? Yes
Problem: A regular octagon has a perimeter of 800m. What is the length of each side?
GPT-3.5 Turbo:
Given that an octagon has 8 sides, we can divide the perimeter by 8 to find the length of each side. Each side of the octagon is 800m / 8 = <<800/8=100>>100m. ### Answer: 100m.
Expected answer: 100
Correct? Yes
Problem: A regular nonagon has a certain side length. If the perimeter of the nonagon is 702 m, what is the length of one side?
GPT-3.5 Turbo:
A regular nonagon has 9 sides, so the perimeter is 9 times the length of one side. Let x be the length of one side. We have the equation: 9x = 702 Dividing both sides by 9, we get: x = 702/9 x = 78 Therefore, the length of one side of the nonagon is 78 m. ### Answer: 78.
Expected answer: 78
Correct? Yes
Problem: A regular nonagon has a perimeter of 855cm. What is the length of one side?
GPT-3.5 Turbo:
Reasoning: A regular nonagon has 9 sides, so each side has the same length. The perimeter of a nonagon is the sum of the lengths of all its sides. Therefore, the length of one side is 855cm / 9 = <<855/9=95>>95cm. ### Answer: 95 cm.
Expected answer: 95
Correct? Yes
Problem: If a regular heptagon has a perimeter of 504 meters, find the length of its side.
GPT-3.5 Turbo:
Reasoning: A regular heptagon has 7 equal sides. Let the length of each side be \( s \) meters. The perimeter of the heptagon is given by \( 7s = 504 \) meters. Solving for \( s \), we have \( s = \frac{504}{7} = 72 \) meters. ### Answer: 72 meters.
Expected answer: 72
Correct? Yes
Problem: A regular nonagon has a perimeter of 657m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: A regular nonagon has 9 sides, so the length of each side is the perimeter divided by the number of sides: 657m / 9 = <<657/9=73>>73m. ### Answer: 73m.
Expected answer: 73
Correct? Yes
Problem: Given a regular octagon where the total perimeter is 48 cm, what is the length of each side?
GPT-3.5 Turbo:
Reasoning: Since a regular octagon has 8 equal sides, we can divide the total perimeter by the number of sides to find the length of each side. Each side of the octagon is 48 cm / 8 = <<48/8=6>>6 cm. ### Answer: 6 cm.
Expected answer: 6
Correct? Yes
Problem: A polygon has eight sides with lengths: 28m, 37m, 51m, 84m, 54m, 31m, 94m, and 12m. If the total perimeter of the polygon is 399m, what is the length of the remaining unknown side?
GPT-3.5 Turbo:
To find the length of the remaining unknown side, we need to subtract the sum of the given side lengths from the total perimeter of the polygon. Sum of the given side lengths = 28 + 37 + 51 + 84 + 54 + 31 + 94 + 12 = 391m Length of the remaining unknown side = Total perimeter - Sum of given side lengths Length of the remaining unknown side = 399 - 391 = 8m ### Answer: 8m.
Expected answer: 8
Correct? Yes
Problem: A regular nonagon has a perimeter of 342m. What is the length of one side?
GPT-3.5 Turbo:
A regular nonagon has 9 sides, so each side has the same length. The perimeter of a nonagon is given by the formula: perimeter = number of sides * length of one side. Given that the perimeter is 342m and the number of sides is 9, we can set up the equation: 342 = 9 * length of one side. Solving for the length of one side, we get: length of one side = 342 / 9 = <<342/9=38>>38 meters. ### Answer: 38 meters.
Expected answer: 38
Correct? Yes
Problem: In a polygon with 8 sides, 7 of the side lengths are given as follows: 7 m, 59 m, 49 m, 38 m, 53 m, 21 m, and 34 m. Given that the total perimeter of the polygon is 330 m, what is the length of the eighth side?
GPT-3.5 Turbo:
Reasoning: To find the length of the eighth side, we need to subtract the sum of the given side lengths from the total perimeter of the polygon. Total perimeter = 330 m Sum of given side lengths = 7 + 59 + 49 + 38 + 53 + 21 + 34 = 261 m Length of the eighth side = 330 - 261 = <<330-261=69>>69 m. ### Answer: 69 m.
Expected answer: 69
Correct? Yes
Problem: A decagon has side lengths of 88m, 96m, 74m, 52m, 45m, 74m, 85m, 85m, and 43m. What is the length of the tenth side if the total perimeter of the decagon is 682m?
GPT-3.5 Turbo:
To find the length of the tenth side, we need to subtract the sum of the lengths of the first nine sides from the total perimeter of the decagon. Sum of the lengths of the first nine sides: 88 + 96 + 74 + 52 + 45 + 74 + 85 + 85 + 43 = 652 Length of the tenth side: 682 - 652 = 30 ### Answer: 30m.
Expected answer: 40
Correct? No
Problem: A regular septagon (7-sided polygon) has a constant perimeter of 161m. If all sides are equal, what is the length of each side?
GPT-3.5 Turbo:
Reasoning: Since a regular septagon has 7 sides, each side has a length of 161m/7 = <<161/7=23>>23m. ### Answer: 23m
Expected answer: 23
Correct? Yes
Problem: A regular hexagon has a perimeter of 324m. What is the length of each side?
GPT-3.5 Turbo:
Given that a regular hexagon has 6 equal sides, we can divide the perimeter by 6 to find the length of each side. Each side length = 324m / 6 = <<324/6=54>>54m. ### Answer: 54m.
Expected answer: 54
Correct? Yes
Problem: A regular pentagon's perimeter is 385 meters. What is the length of one side?
GPT-3.5 Turbo:
Reasoning: A regular pentagon has 5 equal sides. Therefore, the length of one side is the perimeter divided by 5: 385/5 = <<385/5=77>>77 meters. ### Answer: 77 meters.
Expected answer: 77
Correct? Yes
Problem: A regular septagon (7-sided polygon) has a perimeter of 245m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: A regular septagon has 7 equal sides, so the length of each side is the perimeter divided by the number of sides, which is 245m/7 = <<245/7=35>>35m. ### Answer: 35m.
Expected answer: 35
Correct? Yes
Problem: A regular pentagon has a perimeter of 25cm. What is the length of one of its sides?
GPT-3.5 Turbo:
A regular pentagon has 5 equal sides. Perimeter of a regular pentagon = 5 * length of one side. Given perimeter = 25 cm. So, 25 = 5 * length of one side. Dividing both sides by 5, we get: length of one side = 25/5 = <<25/5=5>>5 cm. ### Answer: 5 cm.
Expected answer: 5
Correct? Yes
Problem: A regular hexagon has five of its sides measuring 9m, 49m, 100m, 73m, and 84m respectively. If the total perimeter of the hexagon is 380m, find the length of the sixth side.
GPT-3.5 Turbo:
Reasoning: The total perimeter of the hexagon is the sum of all its sides. Therefore, the length of the sixth side is given by: Length of the sixth side = Total perimeter - Sum of the given sides Length of the sixth side = 380 - (9 + 49 + 100 + 73 + 84) Length of the sixth side = 380 - 315 Length of the sixth side = <<380-315=65>>65m ### Answer: 65m.
Expected answer: 65
Correct? Yes
Problem: An irregular polygon has seven sides with lengths of 23m, 67m, 57m, 94m, 93m, 18m and 30m respectively. If the total perimeter of the polygon is 419m, what is the length of the missing side?
GPT-3.5 Turbo:
To find the length of the missing side, we need to subtract the sum of the given sides from the total perimeter of the polygon. Sum of the given sides = 23 + 67 + 57 + 94 + 93 + 18 + 30 = 382m Length of the missing side = Total perimeter - Sum of given sides Length of the missing side = 419 - 382 = 37m ### Answer: 37m
Expected answer: 37
Correct? Yes
Problem: A regular heptagon (7-sided polygon) has a perimeter of 287m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: Since a regular heptagon has 7 sides, the length of each side is the total perimeter divided by the number of sides. Therefore, the length of each side is 287m / 7 = <<287/7=41>>41m. ### Answer: 41m
Expected answer: 41
Correct? Yes
Problem: A regular pentagon has a perimeter of 55m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: A regular pentagon has 5 equal sides. Therefore, the length of each side is the perimeter divided by 5: 55m / 5 = <<55/5=11>>11m. ### Answer: 11m.
Expected answer: 11
Correct? Yes
Problem: A regular nonagon, which is a nine-sided polygon, has equal side lengths. If the entire perimeter of the nonagon is 657 meters, how long is each side?
GPT-3.5 Turbo:
Reasoning: Since a regular nonagon has nine equal side lengths, each side length is equal to the total perimeter divided by the number of sides, which is 657 meters / 9 sides = <<657/9=73>>73 meters per side. ### Answer: 73 meters.
Expected answer: 73
Correct? Yes
Problem: A regular hexagon has a perimeter of 78m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: A regular hexagon has 6 equal sides, so the length of each side is the perimeter divided by the number of sides, which is 78m/6 = <<78/6=13>>13m. ### Answer: 13m.
Expected answer: 13
Correct? Yes
Problem: A regular octagon has a total perimeter of 600 meters. What is the length of one of its sides?
GPT-3.5 Turbo:
Reasoning: Since an octagon has 8 sides, each side of the octagon is equal in length. Therefore, the length of one side of the octagon is 600/8 = <<600/8=75>>75 meters. ### Answer: 75 meters.
Expected answer: 75
Correct? Yes
Problem: A polygon has side lengths of 39m, 26m, 47m, 52m, 66m, 17m, and 34m. If the overall perimeter of the polygon is 356m, what is the length of the last side?
GPT-3.5 Turbo:
To find the length of the last side, we need to subtract the sum of the given side lengths from the overall perimeter of the polygon. Sum of the given side lengths = 39 + 26 + 47 + 52 + 66 + 17 + 34 = 281m Length of the last side = 356 - 281 = 75m ### Answer: 75m
Expected answer: 75
Correct? Yes
Problem: A regular decagon has a perimeter of 930 cm. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: A regular decagon has 10 sides, so each side has the same length. The perimeter of a decagon is given by the formula: perimeter = number of sides * length of each side. Therefore, the length of each side is perimeter / number of sides = 930 cm / 10 = 93 cm. ### Answer: 93 cm.
Expected answer: 93
Correct? Yes
Problem: A decagon has eight of its sides measuring 24m, 25m, 75m, 38m, 18m, 42m and 61m. If the total perimeter of the decagon is 359m, can you find the length of one of the unknown sides?
GPT-3.5 Turbo:
Let the lengths of the two unknown sides be \( x \) and \( y \) meters. The total perimeter of the decagon is the sum of all the side lengths, so we have: \[ 24 + 25 + 75 + 38 + 18 + 42 + 61 + x + y = 359 \] Solving for \( x + y \), we get: \[ x + y = 359 - (24 + 25 + 75 + 38 + 18 + 42 + 61) \] \[ x + y = 359 - 283 \] \[ x + y = 76 \] Since a decagon has 10 sides, the sum of all side lengths is equal to 10 times the length of one side. Therefore, we have: \[ 24 + 25 + 75 + 38 + 18 + 42 + 61 + x + y = 10 \times \text{length of one side} \] \[ 359 = 10 \times \text{length of one side} \] \[ \text{length of one side} = \frac{359}{10} \] \[ \text{length of one side} = 35.9 \text{ meters} \] ### Answer: The length of one of the unknown sides is 35.9 meters.
Expected answer: 76
Correct? No
Problem: A nonagon has side lengths of 52m, 52m, 44m, 53m, 41m, 91m, 25m, and 2m and the total perimeter of the nonagon is 368m. What is the length of the final side?
GPT-3.5 Turbo:
To find the length of the final side, we need to subtract the sum of the lengths of the other sides from the total perimeter of the nonagon. Sum of the lengths of the other sides = 52 + 52 + 44 + 53 + 41 + 91 + 25 = 358m Length of the final side = Total perimeter - Sum of the lengths of the other sides Length of the final side = 368 - 358 = 10m ### Answer: 10m.
Expected answer: 8
Correct? No
Problem: A regular octagon has a perimeter of 592cm. What is the length of one side?
GPT-3.5 Turbo:
Reasoning: Since a regular octagon has 8 equal sides, we can divide the perimeter by 8 to find the length of one side. Each side length is 592/8 = <<592/8=74>>74 cm. ### Answer: 74 cm.
Expected answer: 74
Correct? Yes
Problem: A regular heptagon has a perimeter of 245m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: A regular heptagon has 7 sides, so the length of each side is the perimeter divided by the number of sides: 245m / 7 = <<245/7=35>>35m. ### Answer: 35m.
Expected answer: 35
Correct? Yes
Problem: A regular decagon has a perimeter of 140m. What is the length of each side?
GPT-3.5 Turbo:
Reasoning: A regular decagon has 10 sides, so the length of each side is the perimeter divided by the number of sides: 140m / 10 = <<140/10=14>>14m. ### Answer: 14m
Expected answer: 14
Correct? Yes
Problem: A polygon has side lengths of 44cm, 5cm, 96cm, 78cm, 49cm, 84cm, 72cm, 74cm, 21cm, and 39cm. If the total perimeter of the polygon is 655cm. What is the length of its 11th side?
GPT-3.5 Turbo:
To find the length of the 11th side, we need to subtract the sum of the first 10 sides from the total perimeter of the polygon. Sum of the first 10 sides = 44 + 5 + 96 + 78 + 49 + 84 + 72 + 74 + 21 + 39 = 562 cm Length of the 11th side = Total perimeter - Sum of the first 10 sides Length of the 11th side = 655 - 562 = 93 cm ### Answer: 93 cm.
Expected answer: 93
Correct? Yes
Problem: A polygon has sides that measure 69m, 81m, 34m, 35m, and 38m respectively. If the polygon's total perimeter is 265m, what is the length of the remaining side?
GPT-3.5 Turbo:
To find the length of the remaining side, we need to subtract the sum of the given sides from the total perimeter of the polygon. Sum of the given sides = 69m + 81m + 34m + 35m + 38m = 257m Length of the remaining side = Total perimeter - Sum of the given sides Length of the remaining side = 265m - 257m = 8m ### Answer: 8m
Expected answer: 8
Correct? Yes
Problem: A pentagon has four of its side lengths as 22m, 14m, 93m, and 75m respectively. If its total perimeter is 234m, find the length of the fifth side.
GPT-3.5 Turbo:
Reasoning: The total perimeter of the pentagon is the sum of all its side lengths. Therefore, the length of the fifth side is: 234m - (22m + 14m + 93m + 75m) = 234m - 204m = <<234-204=30>>30m. ### Answer: 30m.
Expected answer: 30
Correct? Yes