Question

A triangle has sides of lengths 8, 15, and 17. Is it a right triangle? Explain.

a) No; 8^2 + 15^2 = 17^2
b) Yes; 8^2 + 15^2 = 17^2
c) No; 8^2 + 15^2 ≠ 17^2
d) Yes; 8^2 + 15^2 ≠ 17^2

Answer 1

A triangle with sides of lengths 8, 15, and 17 is a right triangle because it satisfies the Pythagorean theorem; the sum of the squares of the two shorter sides equals the square of the longest side (17²).

Step-by-step explanation:

To determine if a triangle with sides of lengths 8, 15, and 17 is a right triangle, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Using the theorem, we calculate:

8² + 15² = 64 + 225 = 289

17² = 289

Since 8² + 15² equals 17², the given triangle satisfies the Pythagorean theorem and is therefore a right triangle. So, the correct answer is:
Yes; 8² + 15² = 17² (option b).