## Geometry: Common Core (15th Edition)

$x = \sqrt {35}$
The altitude of a right triangle is the geometric mean of the lengths of the two hypotenuse segments. Let's set up that proportion: $\frac{a}{x} = \frac{x}{b}$, where $a$ and $b$ are the lengths of the two hypotenuse segments and $x$ is the length of the altitude. Let's plug in our numbers: $\frac{5}{x} = \frac{x}{7}$ Use the cross products property to get rid of the fractions: $x^2 = 35$ Take the positive square root to solve for $x$: $x = \sqrt {35}$