Question
A triangle has side with lengths of 8 inches, 15 inches, and 17 inches is it a right triangle?
Answers
GPT-4o mini
To determine if a triangle with side lengths of 8 inches, 15 inches, and 17 inches is a right triangle, we can use the Pythagorean theorem. According to the theorem, a triangle is a right triangle if the square of the length of the longest side (the hypotenuse) is equal to the sum of the squares of the other two sides.
1. Identify the longest side, which in this case is 17 inches.
2. Calculate the squares of the sides:
- \( 17^2 = 289 \)
- \( 8^2 = 64 \)
- \( 15^2 = 225 \)
3. Now, check if the sum of the squares of the two shorter sides equals the square of the longest side:
\[
8^2 + 15^2 = 64 + 225 = 289
\]
\[
17^2 = 289
\]
Since \( 64 + 225 = 289 \), the triangle with sides of 8 inches, 15 inches, and 17 inches satisfies the Pythagorean theorem.
Therefore, **yes**, the triangle is a right triangle.
1. Identify the longest side, which in this case is 17 inches.
2. Calculate the squares of the sides:
- \( 17^2 = 289 \)
- \( 8^2 = 64 \)
- \( 15^2 = 225 \)
3. Now, check if the sum of the squares of the two shorter sides equals the square of the longest side:
\[
8^2 + 15^2 = 64 + 225 = 289
\]
\[
17^2 = 289
\]
Since \( 64 + 225 = 289 \), the triangle with sides of 8 inches, 15 inches, and 17 inches satisfies the Pythagorean theorem.
Therefore, **yes**, the triangle is a right triangle.