GPT-4o on 3.MD.D.8-triangle
Common Core Standard 3.MD.D.8-triangle
This standard covers the following:
Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
Problem: An equilateral triangle has a perimeter of 990cm. What is the length of each of its sides?
GPT-4o:
An equilateral triangle has all three sides of equal length. To find the length of each side, we need to divide the perimeter by the number of sides.
Given:
- Perimeter of the equilateral triangle = 990 cm
- Number of sides in an equilateral triangle = 3
Let's calculate the length of each side:
\[ \text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} \]
\[ \text{Length of each side} = \frac{990 \text{ cm}}{3} \]
\[ \text{Length of each side} = 330 \text{ cm} \]
### Answer: 330 cm
Expected answer: 330
Correct? Yes
Problem: A triangle has a perimeter of 997m. Two of its sides have lengths of 2m and 667m. What is the length of the third side?
GPT-4o:
To find the length of the third side of the triangle, we need to use the information given about the perimeter and the lengths of the other two sides.
The perimeter of a triangle is the sum of the lengths of all its sides. We can set up the equation as follows:
\[ \text{Perimeter} = \text{Side 1} + \text{Side 2} + \text{Side 3} \]
Given:
- Perimeter = 997 meters
- Side 1 = 2 meters
- Side 2 = 667 meters
Let \( \text{Side 3} \) be \( x \) meters. Then we have:
\[ 997 = 2 + 667 + x \]
To find \( x \), we solve for \( x \):
\[ 997 = 669 + x \]
Subtract 669 from both sides:
\[ 997 - 669 = x \]
\[ 328 = x \]
So, the length of the third side is 328 meters.
### Answer: 328 meters.
Expected answer: 328
Correct? Yes
Problem: An equilateral triangle has a perimeter of 579 cm. What is the length of each of its sides?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides.
Given the perimeter is 579 cm, we calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{3} = \frac{579 \, \text{cm}}{3}
\]
Performing the division:
\[
\frac{579}{3} = 193 \, \text{cm}
\]
### Answer: 193 cm
Expected answer: 193
Correct? Yes
Problem: An equilateral triangle has a perimeter of 684m. What is the length of each of its sides?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides.
Given:
Perimeter = 684 meters
We calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{3} = \frac{684 \, \text{meters}}{3}
\]
Performing the division:
\[
\frac{684}{3} = 228 \, \text{meters}
\]
### Answer: 228 meters
Expected answer: 228
Correct? Yes
Problem: A triangle has a perimeter of 503 meters. One side of the triangle is 223 meters long and another side is 46 meters long. What is the length of the remaining side?
GPT-4o:
To find the length of the remaining side of the triangle, we need to use the information about the perimeter and the lengths of the other two sides.
The perimeter of the triangle is the sum of the lengths of all three sides. We can set up the equation as follows:
\[ \text{Perimeter} = \text{Side 1} + \text{Side 2} + \text{Side 3} \]
Given:
- Perimeter = 503 meters
- Side 1 = 223 meters
- Side 2 = 46 meters
Let \( \text{Side 3} \) be the length of the remaining side. We can write the equation as:
\[ 503 = 223 + 46 + \text{Side 3} \]
To find \( \text{Side 3} \), we need to isolate it on one side of the equation. First, add the lengths of Side 1 and Side 2:
\[ 223 + 46 = 269 \]
Now, substitute this sum back into the equation:
\[ 503 = 269 + \text{Side 3} \]
Next, subtract 269 from both sides to solve for \( \text{Side 3} \):
\[ \text{Side 3} = 503 - 269 \]
Calculate the difference:
\[ \text{Side 3} = 234 \]
### Answer: 234 meters
Expected answer: 234
Correct? Yes
Problem: An equilateral triangle has a perimeter of 105m. What is the length of each of its sides?
GPT-4o:
An equilateral triangle has all three sides of equal length. Let's denote the length of each side as \( s \).
The perimeter of an equilateral triangle is given by the sum of the lengths of its three sides:
\[ \text{Perimeter} = s + s + s = 3s \]
We are given that the perimeter is 105 meters:
\[ 3s = 105 \]
To find the length of each side, we solve for \( s \) by dividing both sides of the equation by 3:
\[ s = \frac{105}{3} \]
\[ s = 35 \]
### Answer: 35 meters
Expected answer: 35
Correct? Yes
Problem: An equilateral triangle has a perimeter of 306cm. What is the length of each of its sides?
GPT-4o:
An equilateral triangle has all three sides of equal length. To find the length of each side, we need to divide the perimeter by the number of sides.
Given:
- Perimeter of the equilateral triangle = 306 cm
- Number of sides in an equilateral triangle = 3
Let's calculate the length of each side:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{306 \, \text{cm}}{3}
\]
\[
\text{Length of each side} = 102 \, \text{cm}
\]
### Answer: 102 cm
Expected answer: 102
Correct? Yes
Problem: An equilateral triangle has a perimeter of 33 cm. What is the length of each of its sides?
GPT-4o:
An equilateral triangle has all three sides of equal length. Let's denote the length of each side as \( s \).
The perimeter of an equilateral triangle is given by the sum of the lengths of its three sides:
\[ \text{Perimeter} = s + s + s = 3s \]
We are given that the perimeter is 33 cm:
\[ 3s = 33 \]
To find the length of each side, we solve for \( s \) by dividing both sides of the equation by 3:
\[ s = \frac{33}{3} \]
\[ s = 11 \]
### Answer: 11 cm
Expected answer: 11
Correct? Yes
Problem: A triangle has a perimeter of 861m. Two of the sides are known to be 192m and 159m in length. Can you find the length of the third side?
GPT-4o:
To find the length of the third side of the triangle, we need to use the information given about the perimeter and the lengths of the other two sides. The perimeter of a triangle is the sum of the lengths of all its sides. We are given: - The perimeter is 861 meters. - Two sides are 192 meters and 159 meters. Let the length of the third side be \( x \). The equation for the perimeter is: \[ 192 + 159 + x = 861 \] First, we add the lengths of the two known sides: \[ 192 + 159 = 351 \] Next, we subtract this sum from the total perimeter to find the length of the third side: \[ x = 861 - 351 \] \[ x = 510 \] ### Answer: 510 meters
Expected answer: 510
Correct? Yes
Problem: A triangle has a perimeter of 489 centimeters. If each of its sides is of equal length, what is the length of one side?
GPT-4o:
To find the length of one side of the triangle, we need to divide the perimeter by the number of sides in the triangle. Since the triangle is equilateral, it has 3 equal sides.
First, we calculate the length of one side:
\[
\text{Length of one side} = \frac{\text{Perimeter}}{3} = \frac{489 \text{ cm}}{3}
\]
Now, we perform the division:
\[
\frac{489}{3} = 163 \text{ cm}
\]
### Answer: 163 cm
Expected answer: 163
Correct? Yes
Problem: An equilateral triangle has a perimeter of 696 meters. What is the length of each side of this triangle?
GPT-4o:
An equilateral triangle has all three sides of equal length. Let's denote the length of each side as \( s \).
The perimeter of an equilateral triangle is given by the formula:
\[ \text{Perimeter} = 3s \]
We are given that the perimeter is 696 meters. Therefore, we can set up the equation:
\[ 3s = 696 \]
To find the length of each side, we divide both sides of the equation by 3:
\[ s = \frac{696}{3} \]
Now, we perform the division:
\[ s = 232 \]
### Answer: 232 meters
Expected answer: 232
Correct? Yes
Problem: The perimeter of a triangle is 804m. One side of the triangle is 180m long, and another side is 579m long. What is the length of the third side?
GPT-4o:
To find the length of the third side of the triangle, we need to use the information given about the perimeter and the lengths of the other two sides.
The perimeter of the triangle is the sum of the lengths of all three sides. We can set up the equation as follows:
\[ \text{Perimeter} = \text{Side 1} + \text{Side 2} + \text{Side 3} \]
Given:
- Perimeter = 804 meters
- Side 1 = 180 meters
- Side 2 = 579 meters
Let \( \text{Side 3} \) be \( x \). Then we have:
\[ 804 = 180 + 579 + x \]
To find \( x \), we solve for \( x \):
\[ 804 = 759 + x \]
Subtract 759 from both sides:
\[ 804 - 759 = x \]
\[ 45 = x \]
So, the length of the third side is 45 meters.
### Answer: 45 meters
Expected answer: 45
Correct? Yes
Problem: An equilateral triangle has a perimeter of 915cm. What is the length of each of its sides?
GPT-4o:
An equilateral triangle has all three sides of equal length. To find the length of each side, we need to divide the perimeter by the number of sides.
Given:
- Perimeter of the equilateral triangle = 915 cm
- Number of sides in an equilateral triangle = 3
Let's calculate the length of each side:
\[ \text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} \]
\[ \text{Length of each side} = \frac{915 \, \text{cm}}{3} \]
\[ \text{Length of each side} = 305 \, \text{cm} \]
### Answer: 305 cm
Expected answer: 305
Correct? Yes
Problem: An equilateral triangle has a perimeter of 564 cm. What is the length of each of its sides?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides.
Given:
Perimeter = 564 cm
We calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{3} = \frac{564 \, \text{cm}}{3} = 188 \, \text{cm}
\]
### Answer: 188 cm
Expected answer: 188
Correct? Yes
Problem: An equilateral triangle has a perimeter of 594 cm. What is the length of each of its sides?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides.
Given:
Perimeter = 594 cm
We calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{3} = \frac{594 \, \text{cm}}{3} = 198 \, \text{cm}
\]
### Answer: 198 cm
Expected answer: 198
Correct? Yes
Problem: An equilateral triangle has a perimeter of 453 cm. How long is each side of the triangle?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides.
Given:
Perimeter = 453 cm
We calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{3} = \frac{453 \, \text{cm}}{3}
\]
Performing the division:
\[
\frac{453}{3} = 151 \, \text{cm}
\]
### Answer: 151 cm
Expected answer: 151
Correct? Yes
Problem: A triangle has a total perimeter of 898m. The lengths of two of its sides are 250m and 435m respectively. Can you find the length of the third side of the triangle?
GPT-4o:
To find the length of the third side of the triangle, we need to subtract the sum of the lengths of the two known sides from the total perimeter. Given: - Total perimeter of the triangle = 898 meters - Length of the first side = 250 meters - Length of the second side = 435 meters First, we calculate the sum of the lengths of the two known sides: \[ 250 + 435 = 685 \] Next, we subtract this sum from the total perimeter to find the length of the third side: \[ 898 - 685 = 213 \] ### Answer: 213 meters
Expected answer: 213
Correct? Yes
Problem: An equilateral triangle has a total perimeter of 405 cm. Can you determine the length of each side?
GPT-4o:
To determine the length of each side of an equilateral triangle, we need to remember that all three sides are equal in length.
Given that the total perimeter of the equilateral triangle is 405 cm, we can set up the following equation:
\[ \text{Perimeter} = \text{Side length} \times 3 \]
Let \( s \) be the length of each side. Therefore, we have:
\[ 3s = 405 \]
To find the length of one side, we divide both sides of the equation by 3:
\[ s = \frac{405}{3} \]
\[ s = 135 \]
So, the length of each side of the equilateral triangle is 135 cm.
### Answer: 135 cm
Expected answer: 135
Correct? Yes
Problem: Somehow you got lost in the forest and got trapped in a mysterious place where you find an equilateral triangle-shaped space. The total perimeter of this space is 612 meters. Can you find out the length of each side of this triangle?
GPT-4o:
To find the length of each side of the equilateral triangle, we start by noting that an equilateral triangle has all three sides of equal length.
Given that the total perimeter of the triangle is 612 meters, we can set up the following equation:
\[ \text{Perimeter} = 3 \times \text{side length} \]
Let \( s \) be the length of each side. Therefore, we have:
\[ 3s = 612 \]
To find \( s \), we divide both sides of the equation by 3:
\[ s = \frac{612}{3} \]
\[ s = 204 \]
Thus, the length of each side of the equilateral triangle is 204 meters.
### Answer: 204 meters
Expected answer: 204
Correct? Yes
Problem: An equilateral triangle has a perimeter of 591 cm. Can you find the length of each side of this triangle?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to remember that all three sides are equal in length. The perimeter of an equilateral triangle is the sum of the lengths of its three sides.
Given:
- Perimeter of the equilateral triangle = 591 cm
Let \( s \) be the length of each side of the equilateral triangle. Since the perimeter is the sum of all three sides, we can write the equation:
\[ 3s = 591 \]
To find the length of one side, we divide the perimeter by 3:
\[ s = \frac{591}{3} \]
Now, we perform the division:
\[ s = 197 \]
So, the length of each side of the equilateral triangle is 197 cm.
### Answer: 197 cm
Expected answer: 197
Correct? Yes
Problem: An equilateral triangle has a perimeter of 858m. What is the length of each of its sides?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides.
Given the perimeter is 858 meters, we calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{3} = \frac{858 \, \text{m}}{3}
\]
Performing the division:
\[
\frac{858}{3} = 286 \, \text{m}
\]
### Answer: 286 meters
Expected answer: 286
Correct? Yes
Problem: An equilateral triangle has a perimeter of 543 meters. What is the length of each of its sides?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides.
Given the perimeter is 543 meters, we calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{3} = \frac{543 \text{ meters}}{3}
\]
Performing the division:
\[
\frac{543}{3} = 181 \text{ meters}
\]
### Answer: 181 meters
Expected answer: 181
Correct? Yes
Problem: A triangle has three equal sides. If the perimeter of the triangle is 255 meters, what is the length of each side?
GPT-4o:
To find the length of each side of the triangle, we start by noting that the triangle is equilateral, meaning all three sides are equal in length.
Given that the perimeter of the triangle is 255 meters, we can set up the following equation:
\[ \text{Perimeter} = \text{Side length} + \text{Side length} + \text{Side length} \]
\[ 255 = 3 \times \text{Side length} \]
To find the length of one side, we divide the perimeter by 3:
\[ \text{Side length} = \frac{255}{3} \]
\[ \text{Side length} = 85 \]
### Answer: 85 meters
Expected answer: 85
Correct? Yes
Problem: An equilateral triangle has a perimeter of 570mm. Find the length of each side of this triangle.
GPT-4o:
To find the length of each side of an equilateral triangle, we need to remember that all three sides are equal in length. The perimeter of an equilateral triangle is the sum of the lengths of its three sides.
Given:
- Perimeter of the equilateral triangle = 570 mm
Let \( s \) be the length of each side of the equilateral triangle. Since the perimeter is the sum of all three sides, we can write the equation:
\[ 3s = 570 \]
To find the length of one side, we divide the perimeter by 3:
\[ s = \frac{570}{3} \]
Now, we perform the division:
\[ s = 190 \]
So, the length of each side of the equilateral triangle is 190 mm.
### Answer: 190 mm
Expected answer: 190
Correct? Yes
Problem: An equilateral triangle has a perimeter of 129m. What is the length of each of its sides?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides.
Given the perimeter is 129 meters, we calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{3} = \frac{129 \, \text{m}}{3} = 43 \, \text{m}
\]
### Answer: 43 m
Expected answer: 43
Correct? Yes
Problem: An equilateral triangle has a perimeter of 858 meters. What is the length of each of its sides?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides.
Given the perimeter is 858 meters, we calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{3} = \frac{858 \text{ meters}}{3}
\]
Performing the division:
\[
\frac{858}{3} = 286 \text{ meters}
\]
### Answer: 286 meters
Expected answer: 286
Correct? Yes
Problem: A triangle has a perimeter of 513 km, and it's known to be an equilateral triangle - meaning all three sides are of equal length. Can you determine how long each side of this triangle is?
GPT-4o:
To determine the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has three sides of equal length.
Given:
- Perimeter of the triangle = 513 km
Since the triangle is equilateral, each side is equal. Therefore, we divide the perimeter by 3:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{3} = \frac{513 \text{ km}}{3}
\]
Performing the division:
\[
\frac{513}{3} = 171 \text{ km}
\]
Thus, each side of the equilateral triangle is 171 km long.
### Answer: 171 km
Expected answer: 171
Correct? Yes
Problem: A triangular field has a perimeter of 828 meters. Two sides of the field are 105 and 434 meters long. How long is the third side of the field?
GPT-4o:
To find the length of the third side of the triangular field, we need to use the perimeter of the triangle. The perimeter is the sum of all three sides of the triangle. Given: - Perimeter of the triangular field = 828 meters - Length of the first side = 105 meters - Length of the second side = 434 meters Let the length of the third side be \( x \) meters. The perimeter of the triangle is the sum of all three sides: \[ 105 + 434 + x = 828 \] To find \( x \), we solve the equation: \[ 105 + 434 + x = 828 \] \[ 539 + x = 828 \] Subtract 539 from both sides to isolate \( x \): \[ x = 828 - 539 \] \[ x = 289 \] ### Answer: 289 meters
Expected answer: 289
Correct? Yes
Problem: The perimeter of a triangle is 773 cm. Two of its sides measure 37 cm and 559 cm, respectively. Find the length of the third side?
GPT-4o:
To find the length of the third side of the triangle, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given: - Perimeter of the triangle = 773 cm - Length of the first side = 37 cm - Length of the second side = 559 cm Let the length of the third side be \( x \) cm. The perimeter of the triangle is the sum of all three sides: \[ 37 + 559 + x = 773 \] To find \( x \), we solve for \( x \): \[ 37 + 559 + x = 773 \] \[ 596 + x = 773 \] \[ x = 773 - 596 \] \[ x = 177 \] ### Answer: 177 cm
Expected answer: 177
Correct? Yes
Problem: An equilateral triangle has a perimeter of 714m. What is the length of each of its sides?
GPT-4o:
An equilateral triangle has all three sides of equal length. To find the length of each side, we can divide the perimeter by the number of sides.
Given:
- Perimeter of the equilateral triangle = 714 meters
- Number of sides in an equilateral triangle = 3
Let's calculate the length of each side:
\[ \text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} \]
\[ \text{Length of each side} = \frac{714 \, \text{m}}{3} \]
\[ \text{Length of each side} = 238 \, \text{m} \]
### Answer: 238 meters
Expected answer: 238
Correct? Yes
Problem: In a large triangular garden, one of its sides is 147m and another side is 590m. If the perimeter of the garden is 792m, can you find the length of the third side?
GPT-4o:
To find the length of the third side of the triangular garden, we need to use the information about the perimeter. The perimeter of a triangle is the sum of the lengths of all its sides. Given: - One side of the triangle = 147 meters - Another side of the triangle = 590 meters - Perimeter of the triangle = 792 meters Let the length of the third side be \( x \) meters. The perimeter of the triangle is the sum of all three sides: \[ 147 + 590 + x = 792 \] To find \( x \), we solve the equation: \[ 147 + 590 + x = 792 \] \[ 737 + x = 792 \] Subtract 737 from both sides to isolate \( x \): \[ x = 792 - 737 \] \[ x = 55 \] So, the length of the third side is 55 meters. ### Answer: 55 meters
Expected answer: 55
Correct? Yes
Problem: The perimeter of a triangle is 871 meters. One of the sides is 321 meters long and another is 528 meters long. What is the length of the third side?
GPT-4o:
To find the length of the third side of the triangle, we need to subtract the lengths of the known sides from the total perimeter. Given: - Perimeter of the triangle = 871 meters - Length of the first side = 321 meters - Length of the second side = 528 meters First, we add the lengths of the two known sides: \[ 321 + 528 = 849 \] Next, we subtract this sum from the total perimeter to find the length of the third side: \[ 871 - 849 = 22 \] ### Answer: 22 meters
Expected answer: 22
Correct? Yes
Problem: A triangle has a perimeter of 991m. Two sides of the triangle measure 424m and 246m respectively. Find the length of the third side of the triangle.
GPT-4o:
To find the length of the third side of the triangle, we need to subtract the sum of the known sides from the perimeter.
First, let's add the lengths of the two known sides:
\[ 424 \, \text{m} + 246 \, \text{m} = 670 \, \text{m} \]
Next, we subtract this sum from the total perimeter:
\[ 991 \, \text{m} - 670 \, \text{m} = 321 \, \text{m} \]
Thus, the length of the third side of the triangle is:
### Answer: 321m
Expected answer: 321
Correct? Yes
Problem: An equilateral triangle has a perimeter of 936m. How long is each side of the triangle?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides.
Given the perimeter is 936 meters, we calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{3} = \frac{936 \, \text{m}}{3}
\]
\[
\text{Length of each side} = 312 \, \text{m}
\]
### Answer: 312 m
Expected answer: 312
Correct? Yes
Problem: A triangle has a perimeter of 721m. Two of its sides have lengths of 204m and 195m, respectively. What is the length of the third side of the triangle?
GPT-4o:
To find the length of the third side of the triangle, we start by using the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given: - Perimeter of the triangle = 721 meters - Length of the first side = 204 meters - Length of the second side = 195 meters Let the length of the third side be \( x \). The perimeter equation is: \[ 204 + 195 + x = 721 \] First, we add the lengths of the first two sides: \[ 204 + 195 = 399 \] Next, we solve for \( x \) by subtracting this sum from the total perimeter: \[ x = 721 - 399 \] \[ x = 322 \] Thus, the length of the third side is 322 meters. ### Answer: 322 meters
Expected answer: 322
Correct? Yes
Problem: An equilateral triangle has a perimeter of 201m. What is the length of each of its sides?
GPT-4o:
An equilateral triangle has all three sides of equal length. Let's denote the length of each side as \( s \).
The perimeter of an equilateral triangle is given by the sum of the lengths of its three sides:
\[ \text{Perimeter} = s + s + s = 3s \]
We are given that the perimeter is 201 meters:
\[ 3s = 201 \]
To find the length of each side, we divide both sides of the equation by 3:
\[ s = \frac{201}{3} \]
\[ s = 67 \]
### Answer: 67 meters
Expected answer: 67
Correct? Yes
Problem: A large equilateral triangle has a perimeter of 756m. Find the length of each of its sides.
GPT-4o:
To find the length of each side of an equilateral triangle, we need to remember that all three sides are equal in length. The perimeter of an equilateral triangle is the sum of the lengths of its three sides.
Given:
- Perimeter of the equilateral triangle = 756 meters
Let \( s \) be the length of each side of the equilateral triangle. Since the perimeter is the sum of all three sides, we can write the equation:
\[ 3s = 756 \]
To find the length of one side, we divide the perimeter by 3:
\[ s = \frac{756}{3} \]
Now, we perform the division:
\[ s = 252 \]
So, the length of each side of the equilateral triangle is 252 meters.
### Answer: 252 meters
Expected answer: 252
Correct? Yes
Problem: The perimeter of a triangle is 923m. Two of its sides are 735m and 144m long respectively. What is the length of the third side?
GPT-4o:
To find the length of the third side of the triangle, we need to subtract the lengths of the two known sides from the perimeter. Given: - Perimeter of the triangle = 923 meters - Length of the first side = 735 meters - Length of the second side = 144 meters Let's denote the length of the third side as \( x \). The perimeter of the triangle is the sum of all three sides: \[ 735 + 144 + x = 923 \] To find \( x \), we solve for \( x \): \[ x = 923 - 735 - 144 \] First, calculate \( 923 - 735 \): \[ 923 - 735 = 188 \] Next, subtract 144 from 188: \[ 188 - 144 = 44 \] So, the length of the third side is: ### Answer: 44 meters.
Expected answer: 44
Correct? Yes
Problem: An equilateral triangle has a perimeter of 813 cm. What is the length of each of its sides?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides. Given: Perimeter = 813 cm Length of each side = Perimeter / Number of sides = 813 cm / 3 = 271 cm ### Answer: 271 cm
Expected answer: 271
Correct? Yes
Problem: An equilateral triangle has a perimeter of 834 feet. What is the length of each of its sides?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides. Given: Perimeter = 834 feet Length of each side = Perimeter / Number of sides = 834 feet / 3 = 278 feet ### Answer: 278 feet
Expected answer: 278
Correct? Yes
Problem: A triangle has a perimeter of 105m and all its sides are equal in length. How long is one side of the triangle?
GPT-4o:
To find the length of one side of the triangle, we need to use the fact that the triangle is equilateral, meaning all three sides are of equal length.
Given:
- Perimeter of the triangle = 105 meters
- Number of sides in a triangle = 3
Since all sides are equal, we can divide the perimeter by the number of sides to find the length of one side.
\[
\text{Length of one side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{105 \, \text{meters}}{3}
\]
\[
\text{Length of one side} = 35 \, \text{meters}
\]
### Answer: 35 meters
Expected answer: 35
Correct? Yes
Problem: A triangle has a perimeter of 195cm. Given that all sides of the triangle are equal, what is the length of each side?
GPT-4o:
To find the length of each side of the triangle, we start by noting that the triangle is equilateral, meaning all three sides are equal in length.
Given:
- Perimeter of the triangle = 195 cm
- Number of sides in a triangle = 3
Since all sides are equal, we can denote the length of each side as \( x \).
The perimeter of an equilateral triangle is given by the sum of all its sides:
\[ 3x = 195 \]
To find \( x \), we divide both sides of the equation by 3:
\[ x = \frac{195}{3} \]
\[ x = 65 \]
Thus, the length of each side of the triangle is 65 cm.
### Answer: 65 cm
Expected answer: 65
Correct? Yes
Problem: A triangle has a perimeter of 919m. You know that one of its sides is 350m long and the other side is 154m long. What is the length of the third side?
GPT-4o:
To find the length of the third side of the triangle, we need to subtract the lengths of the known sides from the total perimeter. Given: - Perimeter of the triangle = 919 meters - Length of the first side = 350 meters - Length of the second side = 154 meters First, we add the lengths of the known sides: \[ 350 + 154 = 504 \] Next, we subtract this sum from the total perimeter to find the length of the third side: \[ 919 - 504 = 415 \] ### Answer: 415 meters
Expected answer: 415
Correct? Yes
Problem: A triangle has a perimeter of 989m. You know that two of its sides are 128m and 288m long respectively. What is the length of the third side?
GPT-4o:
To find the length of the third side of the triangle, we start by using the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given: - Perimeter of the triangle = 989 meters - Length of the first side = 128 meters - Length of the second side = 288 meters Let the length of the third side be \( x \). The perimeter of the triangle is the sum of all three sides: \[ 128 + 288 + x = 989 \] To find \( x \), we solve for \( x \): \[ 128 + 288 + x = 989 \] \[ 416 + x = 989 \] \[ x = 989 - 416 \] \[ x = 573 \] Thus, the length of the third side is 573 meters. ### Answer: 573 meters
Expected answer: 573
Correct? Yes
Problem: An equilateral triangle has a perimeter of 321 meters. If all sides are equal, what is the length of each side of the triangle?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 equal sides.
Given:
- Perimeter of the equilateral triangle = 321 meters
We calculate the length of each side as follows:
\[ \text{Length of each side} = \frac{\text{Perimeter}}{3} \]
\[ \text{Length of each side} = \frac{321 \text{ meters}}{3} \]
\[ \text{Length of each side} = 107 \text{ meters} \]
### Answer: 107 meters
Expected answer: 107
Correct? Yes
Problem: An equilateral triangle has a perimeter of 258 cm. What is the length of each of its sides?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to remember that all three sides are equal in length. The perimeter of an equilateral triangle is the sum of the lengths of its three sides.
Given:
- Perimeter of the equilateral triangle = 258 cm
Let \( s \) be the length of each side of the equilateral triangle. Therefore, the perimeter can be expressed as:
\[ 3s = 258 \]
To find \( s \), we divide both sides of the equation by 3:
\[ s = \frac{258}{3} \]
Now, we perform the division:
\[ s = 86 \]
So, the length of each side of the equilateral triangle is 86 cm.
### Answer: 86 cm
Expected answer: 86
Correct? Yes
Problem: An equilateral triangle has a perimeter of 75m. What is the length of each side of the triangle?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to remember that all three sides are equal in length.
Given that the perimeter of the equilateral triangle is 75 meters, we can set up the following equation:
\[ \text{Perimeter} = \text{Side length} \times 3 \]
Let \( s \) be the length of each side. Therefore, we have:
\[ 3s = 75 \]
To find \( s \), we divide both sides of the equation by 3:
\[ s = \frac{75}{3} \]
\[ s = 25 \]
So, the length of each side of the equilateral triangle is 25 meters.
### Answer: 25 meters
Expected answer: 25
Correct? Yes
Problem: The perimeter of a triangle is 979m. Two of its sides are 620m and 80m respectively. What is the length of the third side?
GPT-4o:
To find the length of the third side of the triangle, we start by using the formula for the perimeter of a triangle, which is the sum of the lengths of all its sides. Given: - Perimeter of the triangle = 979 meters - Length of the first side = 620 meters - Length of the second side = 80 meters Let the length of the third side be \( x \). The perimeter of the triangle can be expressed as: \[ 620 + 80 + x = 979 \] To find \( x \), we solve the equation: \[ 700 + x = 979 \] Subtract 700 from both sides: \[ x = 979 - 700 \] \[ x = 279 \] Thus, the length of the third side is 279 meters. ### Answer: 279 meters.
Expected answer: 279
Correct? Yes
Problem: An equilateral triangle has a perimeter of 966 meters. What is the length of each side of this triangle?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides.
Given the perimeter is 966 meters, we calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{3} = \frac{966 \text{ meters}}{3}
\]
\[
\text{Length of each side} = 322 \text{ meters}
\]
### Answer: 322 meters
Expected answer: 322
Correct? Yes
Problem: An equilateral triangle has a perimeter of 486 cm. What is the length of each of its sides?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides. Given: Perimeter = 486 cm Length of each side = Perimeter / Number of sides Length of each side = 486 cm / 3 Length of each side = 162 cm ### Answer: 162 cm
Expected answer: 162
Correct? Yes
Problem: An equilateral triangle has a perimeter of 948 meters. What is the length of each of its sides?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides.
Given the perimeter is 948 meters, we calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{3} = \frac{948 \text{ meters}}{3}
\]
\[
\text{Length of each side} = 316 \text{ meters}
\]
### Answer: 316 meters
Expected answer: 316
Correct? Yes
Problem: A scalene triangle has three sides of different lengths. The first side is 252m, and the second side is 687m. The total perimeter of the triangle is 998m. Can you find the length of the third side?
GPT-4o:
To find the length of the third side of the scalene triangle, we need to use the information given about the perimeter. The perimeter of a triangle is the sum of the lengths of all its sides. Given: - The first side is 252 meters. - The second side is 687 meters. - The total perimeter is 998 meters. Let the length of the third side be \( x \) meters. The equation for the perimeter is: \[ 252 + 687 + x = 998 \] To find \( x \), we solve for \( x \): \[ 252 + 687 + x = 998 \] \[ 939 + x = 998 \] \[ x = 998 - 939 \] \[ x = 59 \] So, the length of the third side is 59 meters. ### Answer: 59 meters.
Expected answer: 59
Correct? Yes
Problem: An equilateral triangle has a perimeter of 618m. What is the length of each of its sides?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides.
Given:
Perimeter = 618 meters
We calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{3} = \frac{618}{3}
\]
Performing the division:
\[
\frac{618}{3} = 206
\]
### Answer: 206 meters
Expected answer: 206
Correct? Yes
Problem: An equilateral triangle has a perimeter of 483 meters. How long is each side?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides.
Given:
Perimeter = 483 meters
We calculate the length of each side as follows:
\[ \text{Length of each side} = \frac{\text{Perimeter}}{3} \]
\[ \text{Length of each side} = \frac{483}{3} \]
\[ \text{Length of each side} = 161 \]
### Answer: 161 meters
Expected answer: 161
Correct? Yes
Problem: A triangle has a perimeter of 804m. One of its sides is 262m long and another is 90m long. What is the length of the third side?
GPT-4o:
To find the length of the third side of the triangle, we need to subtract the lengths of the known sides from the perimeter. Given: - Perimeter of the triangle = 804 meters - Length of the first side = 262 meters - Length of the second side = 90 meters Let's denote the length of the third side as \( x \). The perimeter of the triangle is the sum of all its sides: \[ 262 + 90 + x = 804 \] To find \( x \), we solve the equation: \[ x = 804 - 262 - 90 \] First, subtract 262 from 804: \[ 804 - 262 = 542 \] Next, subtract 90 from 542: \[ 542 - 90 = 452 \] Therefore, the length of the third side is: ### Answer: 452 meters.
Expected answer: 452
Correct? Yes
Problem: A large triangle has a perimeter of 925m. Two of its sides are 183m and 498m, respectively. What is the length of the third side?
GPT-4o:
To find the length of the third side of the triangle, we need to use the perimeter of the triangle. The perimeter is the sum of all three sides. Given: - Perimeter of the triangle = 925 meters - Length of the first side = 183 meters - Length of the second side = 498 meters Let the length of the third side be \( x \). The perimeter equation is: \[ 183 + 498 + x = 925 \] To find \( x \), we solve for \( x \): \[ 183 + 498 + x = 925 \] \[ 681 + x = 925 \] \[ x = 925 - 681 \] \[ x = 244 \] ### Answer: 244 meters
Expected answer: 244
Correct? Yes
Problem: A scalene triangle has a total perimeter of 573m. One of its sides measures 103m and another side measures 386m. What is the length of the third side?
GPT-4o:
To find the length of the third side of the scalene triangle, we need to subtract the lengths of the known sides from the total perimeter.
Given:
- Total perimeter = 573 meters
- One side = 103 meters
- Another side = 386 meters
First, we add the lengths of the two known sides:
\[ 103 \, \text{m} + 386 \, \text{m} = 489 \, \text{m} \]
Next, we subtract this sum from the total perimeter to find the length of the third side:
\[ 573 \, \text{m} - 489 \, \text{m} = 84 \, \text{m} \]
### Answer: 84 meters
Expected answer: 84
Correct? Yes
Problem: An equilateral triangle has a perimeter of 330m. What is the length of each of its sides?
GPT-4o:
An equilateral triangle has all three sides of equal length. Let's denote the length of each side as \( s \).
The perimeter of an equilateral triangle is given by the sum of the lengths of its three sides:
\[ \text{Perimeter} = s + s + s = 3s \]
We are given that the perimeter is 330 meters:
\[ 3s = 330 \]
To find the length of each side, we solve for \( s \) by dividing both sides of the equation by 3:
\[ s = \frac{330}{3} \]
\[ s = 110 \]
### Answer: 110 meters
Expected answer: 110
Correct? Yes
Problem: A triangle has a perimeter of 850m. Two of its sides have lengths of 57m and 426m, respectively. What is the length of the third side?
GPT-4o:
To find the length of the third side of the triangle, we start by using the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given: - Perimeter of the triangle = 850 meters - Length of the first side = 57 meters - Length of the second side = 426 meters Let the length of the third side be \( x \). The perimeter equation is: \[ 57 + 426 + x = 850 \] First, we add the lengths of the first two sides: \[ 57 + 426 = 483 \] Next, we solve for \( x \) by subtracting this sum from the total perimeter: \[ x = 850 - 483 \] \[ x = 367 \] Thus, the length of the third side is 367 meters. ### Answer: 367 meters
Expected answer: 367
Correct? Yes
Problem: A triangle has a perimeter of 764m. Two of its sides are 265m and 56m in length. What is the length of the third side?
GPT-4o:
To find the length of the third side of the triangle, we need to subtract the lengths of the two known sides from the perimeter. Given: - Perimeter of the triangle = 764 meters - Length of the first side = 265 meters - Length of the second side = 56 meters Let's denote the length of the third side as \( x \). The perimeter of the triangle is the sum of all three sides: \[ 265 + 56 + x = 764 \] To find \( x \), we solve for \( x \): \[ x = 764 - 265 - 56 \] First, subtract 265 from 764: \[ 764 - 265 = 499 \] Next, subtract 56 from 499: \[ 499 - 56 = 443 \] So, the length of the third side is: \[ x = 443 \] ### Answer: 443 meters
Expected answer: 443
Correct? Yes
Problem: An equilateral triangle has a perimeter of 723cm. What is the length of each of its sides?
GPT-4o:
An equilateral triangle has all three sides of equal length. To find the length of each side, we need to divide the perimeter by the number of sides.
Given:
- Perimeter of the equilateral triangle = 723 cm
- Number of sides in an equilateral triangle = 3
Let's calculate the length of each side:
\[ \text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} \]
\[ \text{Length of each side} = \frac{723 \, \text{cm}}{3} \]
\[ \text{Length of each side} = 241 \, \text{cm} \]
### Answer: 241 cm
Expected answer: 241
Correct? Yes
Problem: A triangle has a side with a length of 315m and another side with a length of 100m. If the perimeter of the triangle is 738m, what is the length of the third side?
GPT-4o:
To find the length of the third side of the triangle, we need to use the formula for the perimeter of a triangle. The perimeter \( P \) of a triangle is the sum of the lengths of its three sides. Given: - The length of the first side \( a = 315 \) meters - The length of the second side \( b = 100 \) meters - The perimeter \( P = 738 \) meters Let the length of the third side be \( c \). The formula for the perimeter is: \[ P = a + b + c \] Substituting the given values into the formula: \[ 738 = 315 + 100 + c \] Simplify the equation: \[ 738 = 415 + c \] To find \( c \), subtract 415 from both sides of the equation: \[ c = 738 - 415 \] \[ c = 323 \] ### Answer: 323 meters
Expected answer: 323
Correct? Yes
Problem: A triangle has a perimeter of 762m. If one of the sides measures 131m, and the other side is 147m long, what is the length of the third side?
GPT-4o:
To find the length of the third side of the triangle, we need to use the perimeter of the triangle. The perimeter is the sum of all three sides. Given: - Perimeter of the triangle = 762 meters - Length of the first side = 131 meters - Length of the second side = 147 meters Let the length of the third side be \( x \). The perimeter of the triangle is the sum of all three sides: \[ 131 + 147 + x = 762 \] To find \( x \), we solve for \( x \): \[ 131 + 147 + x = 762 \] \[ 278 + x = 762 \] \[ x = 762 - 278 \] \[ x = 484 \] So, the length of the third side is 484 meters. ### Answer: 484 meters
Expected answer: 484
Correct? Yes
Problem: A triangle has a perimeter of 784m and you know the sum of two of its sides is 472m. What is the length of the third side?
GPT-4o:
To find the length of the third side of the triangle, we can use the information given about the perimeter and the sum of two sides. 1. Let the sides of the triangle be \( a \), \( b \), and \( c \). 2. We know the perimeter of the triangle is 784 meters, so: \[ a + b + c = 784 \] 3. We also know the sum of two of its sides is 472 meters. Let's assume \( a + b = 472 \). To find the length of the third side \( c \), we can substitute \( a + b \) with 472 in the perimeter equation: \[ a + b + c = 784 \] \[ 472 + c = 784 \] Now, solve for \( c \): \[ c = 784 - 472 \] \[ c = 312 \] ### Answer: 312 meters
Expected answer: 312
Correct? Yes
Problem: An equilateral triangle has a perimeter of 543mm. What is the length of each of its sides?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides. Given: Perimeter = 543 mm Length of each side = Perimeter / Number of sides Length of each side = 543 mm / 3 Now, we perform the division: \[ 543 \div 3 = 181 \] ### Answer: 181 mm
Expected answer: 181
Correct? Yes
Problem: A triangle has a first side length of 287m, a second side length of 475m, and a perimeter of 867m. What is the length of the third side?
GPT-4o:
To find the length of the third side of the triangle, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. Given: - First side length = 287 meters - Second side length = 475 meters - Perimeter = 867 meters Let the length of the third side be \( x \). The perimeter of the triangle is the sum of the lengths of all three sides: \[ 287 + 475 + x = 867 \] To find \( x \), we solve for \( x \): \[ 287 + 475 + x = 867 \] \[ 762 + x = 867 \] \[ x = 867 - 762 \] \[ x = 105 \] ### Answer: 105 meters
Expected answer: 105
Correct? Yes
Problem: The perimeter of a triangle is 934m. The lengths of two of its sides add up to 838m (one is 828m and the other is 10m). What is the length of the third side?
GPT-4o:
To find the length of the third side of the triangle, we start by using the information given:
1. The perimeter of the triangle is 934 meters.
2. The lengths of two sides are 828 meters and 10 meters.
First, we add the lengths of the two known sides:
\[ 828 \, \text{m} + 10 \, \text{m} = 838 \, \text{m} \]
Next, we know that the perimeter of the triangle is the sum of all three sides. Therefore, we can find the length of the third side by subtracting the sum of the two known sides from the total perimeter:
\[ 934 \, \text{m} - 838 \, \text{m} = 96 \, \text{m} \]
Thus, the length of the third side is:
### Answer: 96 meters
Expected answer: 96
Correct? Yes
Problem: A triangle has a perimeter of 677m. Two of its sides measure 109m and 530m respectively. What is the length of the third side?
GPT-4o:
To find the length of the third side of the triangle, we need to subtract the sum of the known sides from the perimeter.
Given:
- Perimeter of the triangle = 677 meters
- Length of the first side = 109 meters
- Length of the second side = 530 meters
First, we calculate the sum of the two known sides:
\[ 109 \, \text{m} + 530 \, \text{m} = 639 \, \text{m} \]
Next, we subtract this sum from the perimeter to find the length of the third side:
\[ 677 \, \text{m} - 639 \, \text{m} = 38 \, \text{m} \]
### Answer: 38 meters
Expected answer: 38
Correct? Yes
Problem: An equilateral triangle has a perimeter of 582 cm. What is the length of each of its sides?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides.
Given the perimeter is 582 cm, we calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{3} = \frac{582 \, \text{cm}}{3}
\]
\[
\text{Length of each side} = 194 \, \text{cm}
\]
### Answer: 194 cm
Expected answer: 194
Correct? Yes
Problem: A triangle has a perimeter of 499m. Its largest side is 259m long, and one of the other sides is 11m long. What is the length of the last side?
GPT-4o:
To find the length of the last side of the triangle, we need to use the information given about the perimeter and the lengths of the other two sides.
The perimeter of the triangle is the sum of the lengths of all three sides. We can set up the equation as follows:
\[ \text{Perimeter} = \text{Side 1} + \text{Side 2} + \text{Side 3} \]
Given:
- Perimeter = 499 meters
- Side 1 (largest side) = 259 meters
- Side 2 = 11 meters
Let \( \text{Side 3} \) be the length of the last side. We can write the equation:
\[ 499 = 259 + 11 + \text{Side 3} \]
To find the length of Side 3, we solve for \( \text{Side 3} \):
\[ \text{Side 3} = 499 - 259 - 11 \]
First, subtract 259 from 499:
\[ 499 - 259 = 240 \]
Next, subtract 11 from 240:
\[ 240 - 11 = 229 \]
So, the length of the last side is 229 meters.
### Answer: 229 meters.
Expected answer: 229
Correct? Yes
Problem: An equilateral triangle has a perimeter of 966m. What is the length of each of its sides?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides. Given: Perimeter = 966 meters Length of each side = Perimeter / Number of sides Length of each side = 966 meters / 3 Length of each side = 322 meters ### Answer: 322 meters
Expected answer: 322
Correct? Yes
Problem: An equilateral triangle has a perimeter of 894 inches. What is the length of each side of the triangle?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides.
Given the perimeter is 894 inches, we calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{3} = \frac{894 \text{ inches}}{3}
\]
Performing the division:
\[
\frac{894}{3} = 298
\]
Thus, the length of each side of the equilateral triangle is 298 inches.
### Answer: 298 inches
Expected answer: 298
Correct? Yes
Problem: An equilateral triangle has a perimeter of 891cm. What is the length of each of its sides?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides. Given: Perimeter = 891 cm Length of each side = Perimeter / Number of sides Length of each side = 891 cm / 3 Let's perform the division: \[ 891 \div 3 = 297 \] So, the length of each side of the equilateral triangle is 297 cm. ### Answer: 297 cm
Expected answer: 297
Correct? Yes
Problem: A triangle has a perimeter of 762 meters. Two sides of these triangle are known to be 122 meters and 245 meters long respectively. Can you calculate the length of the third side?
GPT-4o:
To find the length of the third side of the triangle, we need to use the information about the perimeter and the lengths of the two known sides. The perimeter of the triangle is the sum of the lengths of all three sides. Let's denote the length of the third side as \( x \). Given: - Perimeter = 762 meters - First side = 122 meters - Second side = 245 meters The equation for the perimeter is: \[ 122 + 245 + x = 762 \] To find \( x \), we solve for \( x \): \[ x = 762 - 122 - 245 \] First, subtract 122 from 762: \[ 762 - 122 = 640 \] Next, subtract 245 from 640: \[ 640 - 245 = 395 \] So, the length of the third side is: ### Answer: 395 meters.
Expected answer: 395
Correct? Yes
Problem: An equilateral triangle has a perimeter of 411m. What is the length of each side of the triangle?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides.
Given the perimeter is 411 meters, we calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{3} = \frac{411 \, \text{m}}{3}
\]
\[
\text{Length of each side} = 137 \, \text{m}
\]
### Answer: 137 m
Expected answer: 137
Correct? Yes
Problem: A triangle has three identical sides and the total length of the sides is 72m. What is the length of each side of the triangle?
GPT-4o:
To find the length of each side of the triangle, we need to divide the total length of the sides by the number of sides. Since the triangle has three identical sides and the total length is 72 meters, we perform the following calculation:
\[
\text{Length of each side} = \frac{\text{Total length}}{\text{Number of sides}} = \frac{72 \text{ meters}}{3}
\]
\[
\text{Length of each side} = 24 \text{ meters}
\]
### Answer: 24 meters
Expected answer: 24
Correct? Yes
Problem: A large triangle has a perimeter of 930 meters. Two of its sides measure 537 meters and 68 meters respectively. What is the length of the third side?
GPT-4o:
To find the length of the third side of the triangle, we need to subtract the sum of the known sides from the total perimeter.
First, add the lengths of the two known sides:
\[ 537 \text{ meters} + 68 \text{ meters} = 605 \text{ meters} \]
Next, subtract this sum from the total perimeter:
\[ 930 \text{ meters} - 605 \text{ meters} = 325 \text{ meters} \]
Therefore, the length of the third side is:
### Answer: 325 meters
Expected answer: 325
Correct? Yes
Problem: An equilateral triangle has a perimeter of 657 meters. What is the length of each of its sides?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides.
Given the perimeter is 657 meters, we calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{3} = \frac{657 \text{ meters}}{3}
\]
Performing the division:
\[
\frac{657}{3} = 219 \text{ meters}
\]
### Answer: 219 meters
Expected answer: 219
Correct? Yes
Problem: A scalene triangle has a side that measures 368m and another side that measures 230m. If the perimeter of the triangle is 909m, what is the length of the third side?
GPT-4o:
To find the length of the third side of the scalene triangle, we need to use the formula for the perimeter of a triangle. The perimeter \( P \) of a triangle is the sum of the lengths of its three sides.
Given:
- Side 1 = 368 meters
- Side 2 = 230 meters
- Perimeter \( P \) = 909 meters
Let the length of the third side be \( x \).
The formula for the perimeter is:
\[ P = \text{Side 1} + \text{Side 2} + \text{Side 3} \]
Substituting the given values:
\[ 909 = 368 + 230 + x \]
First, add the lengths of the known sides:
\[ 368 + 230 = 598 \]
Now, substitute this sum back into the equation:
\[ 909 = 598 + x \]
To find \( x \), subtract 598 from 909:
\[ x = 909 - 598 \]
\[ x = 311 \]
Therefore, the length of the third side is 311 meters.
### Answer: 311 meters
Expected answer: 311
Correct? Yes
Problem: A triangle has a perimeter of 700 m. Two of its sides are 140m and 525m long. What is the length of the third side?
GPT-4o:
To find the length of the third side of the triangle, we need to use the fact that the perimeter of a triangle is the sum of the lengths of its three sides. Given: - Perimeter of the triangle = 700 meters - Length of the first side = 140 meters - Length of the second side = 525 meters Let the length of the third side be \( x \). The perimeter equation is: \[ 140 + 525 + x = 700 \] To find \( x \), we solve for \( x \): \[ 140 + 525 + x = 700 \] \[ 665 + x = 700 \] \[ x = 700 - 665 \] \[ x = 35 \] So, the length of the third side is 35 meters. ### Answer: 35 meters
Expected answer: 35
Correct? Yes
Problem: A triangle has a perimeter of 915cm. Two of its sides are 484cm and 130cm respectively. What length is the third side of the triangle?
GPT-4o:
To find the length of the third side of the triangle, we need to subtract the lengths of the two known sides from the perimeter.
Given:
- Perimeter of the triangle = 915 cm
- Length of the first side = 484 cm
- Length of the second side = 130 cm
Let's denote the length of the third side as \( x \).
The perimeter of the triangle is the sum of all three sides:
\[ 484 \, \text{cm} + 130 \, \text{cm} + x = 915 \, \text{cm} \]
To find \( x \), we solve for \( x \):
\[ x = 915 \, \text{cm} - 484 \, \text{cm} - 130 \, \text{cm} \]
First, we subtract 484 cm from 915 cm:
\[ 915 \, \text{cm} - 484 \, \text{cm} = 431 \, \text{cm} \]
Next, we subtract 130 cm from 431 cm:
\[ 431 \, \text{cm} - 130 \, \text{cm} = 301 \, \text{cm} \]
Therefore, the length of the third side is:
### Answer: 301 cm
Expected answer: 301
Correct? Yes
Problem: An equilateral triangle has a perimeter of 120 cm. How long is each side of the triangle?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides.
Given the perimeter is 120 cm, we calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{3} = \frac{120 \, \text{cm}}{3} = 40 \, \text{cm}
\]
### Answer: 40 cm
Expected answer: 40
Correct? Yes
Problem: A triangular field has a perimeter of 661m. Two sides of the field are known to be 382m and 151m respectively. What is the length of the third side?
GPT-4o:
To find the length of the third side of the triangular field, we can use the formula for the perimeter of a triangle. The perimeter \( P \) of a triangle is the sum of the lengths of its three sides. Given that the perimeter is 661 meters and two sides are 382 meters and 151 meters, we can set up the equation:
\[ P = \text{side}_1 + \text{side}_2 + \text{side}_3 \]
Substituting the given values:
\[ 661 = 382 + 151 + \text{side}_3 \]
To find the length of the third side, we solve for \(\text{side}_3\):
\[ \text{side}_3 = 661 - 382 - 151 \]
First, we perform the subtraction step-by-step:
\[ 661 - 382 = 279 \]
Then,
\[ 279 - 151 = 128 \]
So, the length of the third side is 128 meters.
### Answer: 128 meters
Expected answer: 128
Correct? Yes
Problem: A triangle has a total perimeter of 678 feet. Two of its sides measure 419 feet and 164 feet respectively. What is the length of the third side?
GPT-4o:
To find the length of the third side of the triangle, we need to subtract the lengths of the two known sides from the total perimeter. Given: - Total perimeter of the triangle = 678 feet - Length of the first side = 419 feet - Length of the second side = 164 feet First, we add the lengths of the two known sides: \[ 419 + 164 = 583 \] Next, we subtract this sum from the total perimeter to find the length of the third side: \[ 678 - 583 = 95 \] ### Answer: 95 feet
Expected answer: 95
Correct? Yes
Problem: The perimeter of a triangle is 248m. Two of the sides are 186m and 37m long, respectively. What is the length of the remaining side?
GPT-4o:
To find the length of the remaining side of the triangle, we need to subtract the lengths of the two known sides from the total perimeter. Given: - Perimeter of the triangle = 248 meters - Length of the first side = 186 meters - Length of the second side = 37 meters Let's denote the length of the remaining side as \( x \). The perimeter of the triangle is the sum of all its sides: \[ 186 + 37 + x = 248 \] To find \( x \), we solve for \( x \): \[ x = 248 - 186 - 37 \] First, subtract 186 from 248: \[ 248 - 186 = 62 \] Next, subtract 37 from 62: \[ 62 - 37 = 25 \] So, the length of the remaining side is: ### Answer: 25 meters.
Expected answer: 25
Correct? Yes
Problem: An equilateral triangle has a perimeter of 246 centimeters. What is the length of each of its sides?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has three equal sides.
Given:
- Perimeter of the equilateral triangle = 246 centimeters
We calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{3} = \frac{246}{3}
\]
Performing the division:
\[
\frac{246}{3} = 82
\]
So, the length of each side of the equilateral triangle is 82 centimeters.
### Answer: 82 centimeters
Expected answer: 82
Correct? Yes
Problem: The total perimeter of a triangular field is 739 meters. Two of its sides measure 180 meters and 338 meters respectively. Find the length of the third side.
GPT-4o:
To find the length of the third side of the triangular field, we start by using the formula for the perimeter of a triangle. The perimeter \( P \) is the sum of the lengths of all three sides. Given: - Total perimeter \( P = 739 \) meters - Length of the first side \( a = 180 \) meters - Length of the second side \( b = 338 \) meters Let the length of the third side be \( c \). The formula for the perimeter is: \[ P = a + b + c \] Substituting the given values into the formula: \[ 739 = 180 + 338 + c \] To find \( c \), we solve for \( c \): \[ c = 739 - 180 - 338 \] First, calculate \( 180 + 338 \): \[ 180 + 338 = 518 \] Then, subtract this sum from the total perimeter: \[ c = 739 - 518 \] \[ c = 221 \] Thus, the length of the third side is 221 meters. ### Answer: 221 meters
Expected answer: 221
Correct? Yes
Problem: An equilateral triangle has a perimeter of 684cm. What is the length of each of its sides?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides.
Given the perimeter is 684 cm, we calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{3} = \frac{684 \, \text{cm}}{3}
\]
Performing the division:
\[
\frac{684}{3} = 228 \, \text{cm}
\]
### Answer: 228 cm
Expected answer: 228
Correct? Yes
Problem: An equilateral triangle has a perimeter of 537m. What is the length of each of its sides?
GPT-4o:
An equilateral triangle has all three sides of equal length. To find the length of each side, we need to divide the perimeter by the number of sides.
Given:
- Perimeter of the equilateral triangle = 537 meters
- Number of sides in an equilateral triangle = 3
Let's calculate the length of each side:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{537 \, \text{m}}{3}
\]
\[
\text{Length of each side} = 179 \, \text{m}
\]
### Answer: 179 meters
Expected answer: 179
Correct? Yes
Problem: A triangle has a perimeter of 568m. The lengths of two of its sides are 110m and 205m. What is the length of the third side?
GPT-4o:
To find the length of the third side of the triangle, we need to subtract the sum of the lengths of the two known sides from the perimeter.
Given:
- Perimeter of the triangle = 568 meters
- Length of the first side = 110 meters
- Length of the second side = 205 meters
First, we calculate the sum of the two known sides:
\[ 110 \, \text{meters} + 205 \, \text{meters} = 315 \, \text{meters} \]
Next, we subtract this sum from the perimeter to find the length of the third side:
\[ 568 \, \text{meters} - 315 \, \text{meters} = 253 \, \text{meters} \]
### Answer: 253 meters
Expected answer: 253
Correct? Yes
Problem: An equilateral triangle has a perimeter of 942mm. What is the length of each of its sides?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides. Given: Perimeter = 942 mm Length of each side = Perimeter / Number of sides Length of each side = 942 mm / 3 Calculating the division: \[ 942 \div 3 = 314 \] ### Answer: 314 mm
Expected answer: 314
Correct? Yes
Problem: A triangular garden has one side that is 325 meters long and another that is 15 meters long. The total perimeter of the triangle is 633 meters. What is the length of the third side of the garden?
GPT-4o:
To find the length of the third side of the triangular garden, we need to use the information about the perimeter. The perimeter of a triangle is the sum of the lengths of all its sides. Given: - One side of the triangle is 325 meters. - Another side of the triangle is 15 meters. - The total perimeter of the triangle is 633 meters. Let the length of the third side be \( x \) meters. The equation for the perimeter is: \[ 325 + 15 + x = 633 \] First, combine the known side lengths: \[ 340 + x = 633 \] Next, solve for \( x \) by subtracting 340 from both sides: \[ x = 633 - 340 \] \[ x = 293 \] Therefore, the length of the third side of the garden is 293 meters. ### Answer: 293 meters
Expected answer: 293
Correct? Yes
Problem: An equilateral triangle has a perimeter of 504 meters. What is the length of each side of the triangle?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides.
Given the perimeter is 504 meters, we calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{3} = \frac{504 \text{ meters}}{3}
\]
\[
\text{Length of each side} = 168 \text{ meters}
\]
### Answer: 168 meters
Expected answer: 168
Correct? Yes
Problem: An equilateral triangle has a perimeter of 51 cm. What is the length of each of its sides?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to remember that all three sides are equal in length.
Given that the perimeter of the equilateral triangle is 51 cm, we can set up the following equation:
\[ \text{Perimeter} = \text{Side length} \times 3 \]
Let \( s \) be the length of each side. Therefore, we have:
\[ 3s = 51 \]
To find \( s \), we divide both sides of the equation by 3:
\[ s = \frac{51}{3} \]
\[ s = 17 \]
So, the length of each side of the equilateral triangle is 17 cm.
### Answer: 17 cm
Expected answer: 17
Correct? Yes
Problem: An equilateral triangle has a perimeter of 501 feet. What is the length of each side of the triangle?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has 3 sides.
Given the perimeter is 501 feet, we calculate the length of each side as follows:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{3} = \frac{501}{3}
\]
Performing the division:
\[
\frac{501}{3} = 167
\]
So, the length of each side of the equilateral triangle is 167 feet.
### Answer: 167 feet
Expected answer: 167
Correct? Yes
Problem: The perimeter of an equilateral triangle is 411 meters. What is the length of each side of the triangle?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to remember that all three sides are equal in length. The perimeter of an equilateral triangle is the sum of the lengths of all three sides.
Given:
- Perimeter of the equilateral triangle = 411 meters
Let \( s \) be the length of each side of the triangle. Since the triangle is equilateral, the perimeter \( P \) can be expressed as:
\[ P = 3s \]
We can set up the equation:
\[ 3s = 411 \]
To find \( s \), we divide both sides of the equation by 3:
\[ s = \frac{411}{3} \]
Calculating the division:
\[ s = 137 \]
Therefore, the length of each side of the equilateral triangle is 137 meters.
### Answer: 137 meters
Expected answer: 137
Correct? Yes
Problem: An equilateral triangle has a perimeter of 114cm. What is the length of each of its sides?
GPT-4o:
An equilateral triangle has all three sides of equal length. To find the length of each side, we need to divide the perimeter by the number of sides.
Given:
- Perimeter of the equilateral triangle = 114 cm
- Number of sides in a triangle = 3
Let's calculate the length of each side:
\[ \text{Length of each side} = \frac{\text{Perimeter}}{\text{Number of sides}} \]
\[ \text{Length of each side} = \frac{114 \, \text{cm}}{3} \]
\[ \text{Length of each side} = 38 \, \text{cm} \]
### Answer: 38 cm
Expected answer: 38
Correct? Yes
Problem: An equilateral triangle has a perimeter of 69m. What is the length of each of its sides?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to remember that all three sides are equal in length.
Given that the perimeter of the equilateral triangle is 69 meters, we can set up the following equation:
\[ \text{Perimeter} = \text{Side length} \times 3 \]
Let \( s \) be the length of each side. Therefore, we have:
\[ 3s = 69 \]
To find \( s \), we divide both sides of the equation by 3:
\[ s = \frac{69}{3} \]
\[ s = 23 \]
So, the length of each side of the equilateral triangle is 23 meters.
### Answer: 23 meters
Expected answer: 23
Correct? Yes
Problem: A triangle has sides of lengths 464m and 377m respectively. If the total perimeter of the triangle is 907m, what is the length of the third side?
GPT-4o:
To find the length of the third side of the triangle, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all its sides. Given: - The lengths of two sides are 464 meters and 377 meters. - The total perimeter of the triangle is 907 meters. Let the length of the third side be \( x \). The perimeter of the triangle is given by: \[ 464 + 377 + x = 907 \] To find \( x \), we solve for \( x \): \[ 464 + 377 + x = 907 \] \[ 841 + x = 907 \] \[ x = 907 - 841 \] \[ x = 66 \] ### Answer: 66 meters
Expected answer: 66
Correct? Yes
Problem: An equilateral triangle has a perimeter of 966m. What is the length of each of its sides?
GPT-4o:
To find the length of each side of an equilateral triangle, we need to divide the perimeter by the number of sides. An equilateral triangle has three equal sides.
Given:
Perimeter = 966 meters
Since the triangle is equilateral, each side is equal. Therefore, we divide the perimeter by 3:
\[
\text{Length of each side} = \frac{\text{Perimeter}}{3} = \frac{966 \, \text{m}}{3}
\]
Performing the division:
\[
\frac{966}{3} = 322 \, \text{m}
\]
### Answer: 322 meters
Expected answer: 322
Correct? Yes