In a right triangle with legs 5 and 12, what is the hypotenuse?

• A. 5
• B. 12
• C. 15
• D. 13

Answer: (D)

In a right triangle, the hypotenuse is found using the Pythagorean relation c^2 = a^2 + b^2, where a and b are the legs. With legs 5 and 12, the hypotenuse is c = sqrt(5^2 + 12^2) = sqrt(25 + 144) = sqrt(169) = 13. The hypotenuse must be the longest side, and 13 is longer than both 5 and 12, which fits this role. This is a well-known 5-12-13 right triangle. So the hypotenuse is 13.