Answer
$x = 2 \sqrt {13}$
Work Step by Step
We know that each leg of the triangle is the geometric mean of the hypotenuse and the hypotenuse that is adjacent to that leg:
$\frac{a}{y} = \frac{y}{b}$, where $a$ and $b$ are the length of the hypotenuse and the length of the segment of the hypotenuse closest to the leg, and $y$ is the length of the leg.
$\frac{9 + 4}{x} = \frac{x}{4}$
Evaluate what is in brackets first:
$\frac{13}{x} = \frac{x}{4}$
Use the cross products property to get rid of the fractions:
$x^2 = 52$
Rewrite $52$ as the product of a perfect square and another factor:
$x^2 = 4 • 13$
Take the positive square root to solve for $x$:
$x = 2 \sqrt {13}$
