Answer
$x = 12$
Work Step by Step
The altitude of a right triangle is the geometric mean of the lengths of the two hypotenuse segments. Let's set up that proportion:
The geometric mean of two numbers can be found using the following 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:
$\frac{9}{x} = \frac{x}{16}$
Use the cross products property to get rid of the fractions:
$x^2 = 144$
Take the positive square root to solve for $x$:
$x = 12$
