Question

What is the length of the hypotenuse of a right triangle if the two other sides are of lengths 5 and 11?

Answer 1

`sqrt146`

Explanation:

This is a job for the Pythagorean Theorem.

The Pythagorean Theorem takes the length of any two sides of a right triangle and tells you the length of the remaining side.

For a right triangle with leg lengths of `a` and `b` and a hypotenuse length of `c`, the Pythagorean Theorem states that

`a^2+b^2=c^2`

Here, we are given the two sides that are not the hypotenuse, which are `a` and `b`. We can substitute them into the equation to find the length of the hypotenuse, `c`.

`5^2+11^2=c^2`

Simplify.

`25+121=c^2`

`146=c^2`

`c=sqrt146`

This is as simplified as it can get, since the prime factorization of `146` is `2*73`.