Question #N549
A triangle has sides of length 5, 12, and 13. Is this triangle 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 square of the length of the longest side is equal to the sum of the squares of the lengths of the other two sides. In this case, the longest side is 13, and $5^2 + 12^2 = 25 + 144 = 169 = 13^2$, so the triangle is a right triangle.