Question #N922
The lengths of the sides of a triangle are 5, 12, and 13. Is this triangle a right triangle? Explain your reasoning.
A. Yes, because the triangle satisfies the Pythagorean Theorem: 5^2 + 12^2 = 13^2.
B. Yes, because the triangle has one angle that measures 90 degrees.
C. No, because the triangle is not a right triangle, and the angles do not measure 90 degrees.
D. No, because the triangle does not satisfy the Pythagorean Theorem: 5^2 + 12^2 ≠13^2.
Correct Answer is: A
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, 5^2 + 12^2 = 25 + 144 = 169, and 13^2 = 169. Since the sides satisfy the Pythagorean Theorem, the triangle is a right triangle.