Answer
$x = 2\sqrt {14}$
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.
Let's plug in what we know into the Pythagorean theorem:
$x^2 + 13^2 = 15^2$
Evaluate the exponents:
$x^2 + 169 = 225$
Subtract $169$ from each side of the equation:
$56 = x^2$
Rewrite $56$ as the product of a perfect square and another factor:
$x^2 = 4 • 14$
Take the positive square root to solve for $x$:
$x = 2\sqrt {14}$
