The lengths of the sides of different triangles are given below. Which is a right triangle?
A) 5, 12, 12
B) 9, 7, 10
C) 6, 13, 14
D) 5, 12, 13
E) 9, 7, 11

Question

Quizplus · Accepted Answer

In a right triangle, the sum of the squares of the two smaller sides is equal to the square of the largest side (also known as the hypotenuse).
Using this rule, we can check the options:
- Option A: 5^2 + 12^2 = 169, 12^2 = 144, not a right triangle
- Option B: 9^2 + 7^2 = 130, 10^2 = 100, not a right triangle
- Option C: 6^2 + 13^2 = 205, 14^2 = 196, not a right triangle
- Option D: 5^2 + 12^2 = 169, 13^2 = 169, a right triangle
- Option E: 9^2 + 7^2 = 130, 11^2 = 121, not a right triangle

Therefore, the answer is D.

The Lengths of the Sides of Different Triangles Are Given