What is the length of the hypotenuse in a right triangle with sides of length 5 and 12?

To find the length of the hypotenuse in a right triangle with two known side lengths (5 and 12), we can apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula can be written as:

c² = a² + b²

In this case, you can substitute the given side lengths into the formula:

c² = 5² + 12²

c² = 25 + 144

c² = 169

To find c, which represents the hypotenuse, we need to take the square root of 169:

c = √169

c = 13

Thus, the length of the hypotenuse is 13, making this the correct answer. This calculation demonstrates how the side lengths of a right triangle relate to one another through the Pythagorean theorem, allowing one to determine the length of the hypotenuse based on the other two sides.