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

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

• A. 5
• B. 4
• C. 3
• D. √13

Answer: (A)

In a right triangle, the hypotenuse is the longest side and its length follows the Pythagorean theorem: the square of the hypotenuse equals the sum of the squares of the legs. Here, with legs 3 and 4, the hypotenuse is c = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5. The hypotenuse must be longer than each leg, and 5 satisfies that, making it the correct length. The other options either correspond to the leg lengths themselves or would give a value shorter than a leg (for example, sqrt(13) is about 3.61, which is not possible for the hypotenuse when one leg is 4).

In a right triangle, the hypotenuse is the longest side and its length follows the Pythagorean theorem: the square of the hypotenuse equals the sum of the squares of the legs. Here, with legs 3 and 4, the hypotenuse is c = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5. The hypotenuse must be longer than each leg, and 5 satisfies that, making it the correct length. The other options either correspond to the leg lengths themselves or would give a value shorter than a leg (for example, sqrt(13) is about 3.61, which is not possible for the hypotenuse when one leg is 4).