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

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

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Answer 1 · 2016-02-11T01:51:00

$sqrt146$

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 $2*73$ .

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

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