If the legs of a right triangle measure 5 and 12, what is the length of the hypotenuse?

• A. 12
• B. 5
• C. 13
• D. 10

Answer: (C)

In a right triangle, the hypotenuse length is found by the Pythagorean theorem: the square of the hypotenuse equals the sum of the squares of the two legs. Here, with legs 5 and 12, the hypotenuse squared is 5^2 + 12^2 = 25 + 144 = 169, so the hypotenuse is √169 = 13. This is the classic 5-12-13 right triangle. The other numbers don’t fit as the hypotenuse with these leg lengths—12 and 5 would be the legs, and 10 would require different leg lengths (for example, 6 and 8) to produce a hypotenuse of 10.