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

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

• A. 5
• B. 12
• C. 10
• D. 13

Answer: (D)

In a right triangle, the longest side is the hypotenuse, and its length comes from the Pythagorean theorem: the square of the hypotenuse equals the sum of the squares of the two legs. So with legs measuring 5 and 12, the calculation is c^2 = 5^2 + 12^2 = 25 + 144 = 169. Taking the square root gives c = 13. So the hypotenuse is 13. The other numbers are just the legs, or come from a different triple (for example, 10 can be the hypotenuse of a 6-8-10 triangle), but not for these two legs.

In a right triangle, the longest side is the hypotenuse, and its length comes from the Pythagorean theorem: the square of the hypotenuse equals the sum of the squares of the two legs. So with legs measuring 5 and 12, the calculation is c^2 = 5^2 + 12^2 = 25 + 144 = 169. Taking the square root gives c = 13. So the hypotenuse is 13. The other numbers are just the legs, or come from a different triple (for example, 10 can be the hypotenuse of a 6-8-10 triangle), but not for these two legs.