In a right triangle with legs 3 and 4, the length of the hypotenuse is which of the following?

In a right triangle with legs 3 and 4, the length of the hypotenuse is which of the following?

• A. 5
• B. 6
• C. 7
• D. 9

Answer: (A)

In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs. Here, the legs are 3 and 4, so 3^2 + 4^2 = 9 + 16 = 25. The hypotenuse is the square root of that, which is 5. This is a classic 3-4-5 triangle, so 5 fits perfectly as the longest side. The other options would require the hypotenuse squared to be 36, 49, or 81, which don’t match 25, so they can’t be correct.

In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs. Here, the legs are 3 and 4, so 3^2 + 4^2 = 9 + 16 = 25. The hypotenuse is the square root of that, which is 5. This is a classic 3-4-5 triangle, so 5 fits perfectly as the longest side. The other options would require the hypotenuse squared to be 36, 49, or 81, which don’t match 25, so they can’t be correct.