# If the hypotenuse of a triangle is 30 inches and one of the legs is 10 in, how long is the other leg?

Mar 17, 2018

The leg is $20 \sqrt{2}$

#### Explanation:

We'll solve this using the Pythagorean Theorem.

${a}^{2} + {b}^{2} = {c}^{2}$
where $a$ and $b$ are the length of the legs , and $c$ is the length of the hypotenuse.

Let's plug in the values in the question:
${a}^{2} + {b}^{2} = {c}^{2}$
${10}^{2} + {b}^{2} = {30}^{2}$
$100 + {b}^{2} = 900$
${b}^{2} = 800$
$b = \sqrt{800}$

Now simplify $\sqrt{800}$ to find the exact length:
sqrt800=sqrt(2×2^2×(2×5)^2)=2×2×5×sqrt2=20sqrt2

The length of the side is $20 \sqrt{2}$