What is the hypotenuse of a right triangle with legs 5 and 12?

What is the hypotenuse of a right triangle with legs 5 and 12?

• A. 5
• B. 12
• C. 10
• D. 13

Answer: (D)

In a right triangle, the hypotenuse is found using the Pythagorean theorem: the square of the hypotenuse equals the sum of the squares of the legs. With legs 5 and 12, compute 5^2 + 12^2 = 25 + 144 = 169, so the hypotenuse is sqrt(169) = 13. The hypotenuse is the longest side, so it must be larger than both legs; 13 fits that requirement and aligns with the known 5-12-13 right triangle. The other numbers don’t work because they are not the correct length for the longest side given these legs (for example, 5 and 12 are the legs themselves, and 10 is shorter than one leg, which can’t be the hypotenuse).

In a right triangle, the hypotenuse is found using the Pythagorean theorem: the square of the hypotenuse equals the sum of the squares of the legs. With legs 5 and 12, compute 5^2 + 12^2 = 25 + 144 = 169, so the hypotenuse is sqrt(169) = 13. The hypotenuse is the longest side, so it must be larger than both legs; 13 fits that requirement and aligns with the known 5-12-13 right triangle. The other numbers don’t work because they are not the correct length for the longest side given these legs (for example, 5 and 12 are the legs themselves, and 10 is shorter than one leg, which can’t be the hypotenuse).