A right triangle has legs 8 and 15. What is the length of the hypotenuse?

A right triangle has legs 8 and 15. What is the length of the hypotenuse?

• A. 13
• B. 17
• C. 21
• D. 19

Answer: (B)

In a right triangle, the hypotenuse length comes from the Pythagorean theorem: the sum of the squares of the legs equals the square of the hypotenuse. Here the legs are 8 and 15, so 8^2 + 15^2 = 64 + 225 = 289. The hypotenuse is the square root of that, which is √289 = 17. This 8-15-17 relationship is a classic Pythagorean triple, which is why 17 fits exactly. The other numbers don’t satisfy the equation because their squares don’t add up to 289.

In a right triangle, the hypotenuse length comes from the Pythagorean theorem: the sum of the squares of the legs equals the square of the hypotenuse. Here the legs are 8 and 15, so 8^2 + 15^2 = 64 + 225 = 289. The hypotenuse is the square root of that, which is √289 = 17. This 8-15-17 relationship is a classic Pythagorean triple, which is why 17 fits exactly. The other numbers don’t satisfy the equation because their squares don’t add up to 289.