Answer
$x = 12\sqrt 2$
Work Step by Step
We can find the third side by using the Pythagorean theorem, which states that $a^2 + b^2 = c^2$, where $a$ and $b$ are the legs of the right triangle and $c$ is the hypotenuse. Both legs have lengths of $12$ because they are marked as congruent.
Let's plug in what we know into the Pythagorean theorem:
$12^2 + 12^2 = x^2$
Evaluate the exponents:
$144 + 144 = x^2$
Add to simplify:
$288 = x^2$
Rewrite $288$ as the product of a perfect square and another factor:
$x^2 = 144 • 2$
Take the positive square root to solve for $x$:
$x = 12\sqrt 2$
