The legs of a right triangle are 7 and 11 inches long, respectively. What is the length of the hypotenuse?

Mar 23, 2018

$\sqrt{170}$, or $13.0384$...

Explanation:

You know that the Pythagorean Theorem is:

${a}^{2} + {b}^{2} = {c}^{2}$,
Where:
$a$ is the length of one of the legs,
$b$ is the length of the other leg, and
$c$ is the length of the hypotenuse.

You know the lengths of the two legs are $7$ and $11$, so we'll say that $a$ is $7$, and $b$ is $11$.

Knowing that, we can plug those into our equation and simplify like so:

${7}^{2} + {11}^{2} = {c}^{2}$
$49 + 121 = {c}^{2}$
$170 = {c}^{2}$
$\sqrt{170} = c = 13.0384 \ldots$

Hope this helped!