# How do you find the lengths of the sides of a right triangle given the legs x and x and the hypotenuse 8?

Mar 7, 2016

$x = 4 \sqrt{2}$

#### Explanation:

The Pythagorean Theorem gives the relations between the legs $a , b$ and hypotenuse $c$ of a right triangle:

${a}^{2} + {b}^{2} = {c}^{2}$

Here, since the legs are both $x$, $a = x$ and $b = x$, and since the hypotenuse is $8$, $c = 8$.

${x}^{2} + {x}^{2} = {8}^{2}$

Combine the ${x}^{2}$ terms. Recall that ${8}^{2} = 64$.

$2 {x}^{2} = 64$

Divide both sides by $2$.

${x}^{2} = 32$

Take the square root of both sides. (Only take the positive root--a negative side length wouldn't make any sense.)

$x = \sqrt{32}$

Simplify the term in the square root.

$x = \sqrt{16} \sqrt{2}$

$x = 4 \sqrt{2}$