Geometry: Common Core (15th Edition)

$x = 8$
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 $x$: $x = 8$