Answer
$B$
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:
$\frac{a}{x} = \frac{x}{b}$, 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:
$\frac{5}{x} = \frac{x}{15}$
Use the cross products property to get rid of the fractions:
$x^2 = 75$
Rewrite $75$ as the product of a perfect square and another factor:
$x^2 = 25 • 3$
Take the positive square root of each factor to solve for $x$:
$x = 5 \sqrt {3}$
The answer is $B$.
