Chapter 8.1, Problem 20PPS

To determine

The value of x, y and z.

Answer to Problem 20PPS

  $\begin{array}{l}y=2\sqrt{6}\\ x=2\sqrt{10}\\ z=2\sqrt{15}\end{array}$

Explanation of Solution

Given:

The given figure is:

Calculation:

According to Geometric Mean Altitude Theorem,

  $\begin{array}{l}y=\sqrt{4\left(6\right)}\\ y=\sqrt{24}\\ y=2\sqrt{6}\end{array}$

According to Geometric Mean Leg Theorem,

  $\begin{array}{l}x=\sqrt{4\left(4+6\right)}\\ x=\sqrt{4\left(10\right)}\\ x=\sqrt{40}\\ x=2\sqrt{10}\\ \text{and}\\ z=\sqrt{6\left(4+6\right)}\\ z=\sqrt{6\left(10\right)}\\ z=\sqrt{60}\\ z=2\sqrt{15}\end{array}$