In a right triangle, if the legs are 3 and 4, what is the hypotenuse?

In a right triangle, if the legs are 3 and 4, what is the hypotenuse?

• A. 5
• B. 6
• C. 7
• D. 3

Answer: (A)

In a right triangle, the longest side, the hypotenuse, satisfies the Pythagorean theorem: the square of the hypotenuse equals the sum of the squares of the legs. Here, the legs are 3 and 4, so compute 3^2 + 4^2 = 9 + 16 = 25. The hypotenuse is the square root of that, sqrt(25) = 5. This is the classic 3-4-5 right triangle, where the hypotenuse is the longest side. The other options don’t fit because 6 or 7 would imply larger sums of squares than 25, and 3 cannot be the hypotenuse since it isn’t longer than the legs. Therefore, the hypotenuse is 5.

In a right triangle, the longest side, the hypotenuse, satisfies the Pythagorean theorem: the square of the hypotenuse equals the sum of the squares of the legs. Here, the legs are 3 and 4, so compute 3^2 + 4^2 = 9 + 16 = 25. The hypotenuse is the square root of that, sqrt(25) = 5. This is the classic 3-4-5 right triangle, where the hypotenuse is the longest side. The other options don’t fit because 6 or 7 would imply larger sums of squares than 25, and 3 cannot be the hypotenuse since it isn’t longer than the legs. Therefore, the hypotenuse is 5.