Question

in 21–23, the altitude to the hypotenuse of a right triangle divides the hypotenuse into two segments. 21) if the lengths of the segments are 5 inches and 20 inches, find the length of the altitude.

Explanation:

Step1: Recall the geometric mean theorem

In a right - triangle, if the altitude \(h\) to the hypotenuse divides the hypotenuse into two segments \(a\) and \(b\), then \(h=\sqrt{ab}\).

Step2: Substitute the given values

Here, \(a = 5\) inches and \(b=20\) inches. So, \(h=\sqrt{5\times20}\).

$$
LATEXBLOCK0
$$

Answer:

The length of the altitude is \(10\) inches.