In a right triangle with legs 3 and 4, the hypotenuse is which value?

In a right triangle with legs 3 and 4, the hypotenuse is which value?

• A. 3
• B. 4
• C. 5
• D. 6

Answer: (C)

In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs. With legs 3 and 4, you get 3^2 + 4^2 = 9 + 16 = 25. The hypotenuse is the positive square root of that, so c = sqrt(25) = 5. This matches the well-known 3-4-5 triangle, where the longest side is 5. A hypotenuse must be longer than each leg, and 5 fits the Pythagorean relation for these legs; 3 or 4 wouldn’t satisfy the required sum, and 6 would not match 25.

In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs. With legs 3 and 4, you get 3^2 + 4^2 = 9 + 16 = 25. The hypotenuse is the positive square root of that, so c = sqrt(25) = 5. This matches the well-known 3-4-5 triangle, where the longest side is 5. A hypotenuse must be longer than each leg, and 5 fits the Pythagorean relation for these legs; 3 or 4 wouldn’t satisfy the required sum, and 6 would not match 25.