Chapter 8.3, Problem 58SPR

To determine

The value of x, y and z.

Answer to Problem 58SPR

  $\begin{array}{l}y=6.9\\ x=8\sqrt{3}=13.9\\ z=8\end{array}$

Explanation of Solution

Given:

The given figure is:

Calculation:

According to Geometric Mean Altitude Theorem,

  $\begin{array}{l}y=\sqrt{12\left(4\right)}\\ y=\sqrt{48}\\ y=4\sqrt{3}\\ y=6.9\end{array}$

According to Geometric Mean Leg Theorem,

  $\begin{array}{l}x=\sqrt{12\left(12+4\right)}\\ x=\sqrt{12\left(16\right)}\\ x=\sqrt{192}\\ x=8\sqrt{3}=13.9\\ \text{and}\\ z=\sqrt{4\left(12+4\right)}\\ z=\sqrt{4\left(16\right)}\\ z=\sqrt{64}\\ z=8\end{array}$