Chapter 8, Problem 14SGR

To determine

The value of x, y and z.

Answer to Problem 14SGR

  $\begin{array}{l}x=2\sqrt{13}\\ y=3\sqrt{13}\\ z=6\end{array}$

Explanation of Solution

Given:

The given figure is:

Calculation:

According to Geometric Mean Altitude Theorem,

  $\begin{array}{l}z=\sqrt{4\left(9\right)}\\ z=\sqrt{36}\\ z=6\end{array}$

According to Geometric Mean Leg Theorem,

  $\begin{array}{l}y=\sqrt{9\left(9+4\right)}\\ y=\sqrt{9\left(13\right)}\\ y=\sqrt{117}\\ y=3\sqrt{13}\\ \text{and}\\ x=\sqrt{4\left(9+4\right)}\\ x=\sqrt{4\left(13\right)}\\ x=\sqrt{52}\\ x=2\sqrt{13}\end{array}$