If a right triangle has legs 3 and 4, what is the length of the hypotenuse?

If a right triangle has legs 3 and 4, what is the length of the hypotenuse?

• A. 6
• B. 4
• C. √13
• D. 5

Answer: (D)

In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs. With legs of 3 and 4, compute 3^2 + 4^2 = 9 + 16 = 25. The hypotenuse h satisfies h^2 = 25, so h = 5. This is the classic 3-4-5 triangle, where the longest side is 5. The other options don’t fit because they don’t satisfy h^2 = 25: 6 would give h^2 = 36, 4 isn’t larger than both legs, and √13 is about 3.61, not larger than the longer leg. So the length is 5.

In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs. With legs of 3 and 4, compute 3^2 + 4^2 = 9 + 16 = 25. The hypotenuse h satisfies h^2 = 25, so h = 5. This is the classic 3-4-5 triangle, where the longest side is 5. The other options don’t fit because they don’t satisfy h^2 = 25: 6 would give h^2 = 36, 4 isn’t larger than both legs, and √13 is about 3.61, not larger than the longer leg. So the length is 5.