Question #N323
A triangle has sides of length 5, 12, and 13. Is this a right triangle? Explain your reasoning.
A. Yes, because 5^2 + 12^2 = 13^2.
B. Yes, because 5 + 12 = 13.
C. No, because 5^2 + 12^2 \neq 13^2.
D. No, because 5 + 12 \neq 13.
Correct Answer is: A
A triangle is a right triangle if and only if the sum of the squares of the two shorter sides is equal to the square of the longest side. In this case, 5^2 + 12^2 = 25 + 144 = 169, and 13^2 = 169. Therefore, the triangle is a right triangle.