Question #N46

A triangle has sides of length 5, 12, and 13. Is this triangle a right triangle? Explain your reasoning.
A. Yes, because the triangle satisfies the Pythagorean Theorem.
B. Yes, because the triangle has two equal sides.
C. No, because the triangle does not satisfy the Pythagorean Theorem.
D. No, because the triangle has one side that is longer than the sum of the other two sides.

Correct Answer is: A

Yes, the triangle is a right triangle because it satisfies the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, 5² + 12² = 25 + 144 = 169, and 13² = 169. Since the square of the longest side (13) is equal to the sum of the squares of the other two sides (5 and 12), the triangle is a right triangle.