Textbook Problem

Note: Exercises preceded by an asterisk are of a more challenging nature.

In Exercises 39 and 42, refer to the line segments shown.

Use the following theorem to construct the geometric mean of the numerical lengths of the segments $\stackrel{-}{WX}$ and $\stackrel{-}{YZ}$.

Theorem: The length of the altitude to the hypotenuse of a right triangle is the geometric mean between the lengths of the segments of the hypotenuse.