Answer
$x = 8$
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.
$\frac{32}{16} = \frac{16}{x}$
Use the cross products property to get rid of the fractions:
$32x = 256$
Divide each side by $32$ to solve for $x$:
$x = 8$
