Chapter 8.1, Problem 6CYU

To determine

The value of x, y and z.

Answer to Problem 6CYU

  $\begin{array}{l}x=32\\ y=8\sqrt{5}\\ y=16\sqrt{5}\end{array}$

Explanation of Solution

Given:

  

Calculation:

According to Geometric Mean Altitude Theorem,

  $\begin{array}{l}16=\sqrt{x\left(8\right)}\\ 256=8x\\ x=\frac{256}{8}\\ x=32\end{array}$

According to Geometric Mean Leg Theorem,

  $\begin{array}{l}z=\sqrt{8\left(8+32\right)}\\ z=\sqrt{8\left(40\right)}\\ z=\sqrt{2\times 2\times 2\times 2\times 2\times 2\times 5}\\ z=8\sqrt{5}\\ \text{and}\\ y=\sqrt{32\left(8+32\right)}\\ y=\sqrt{32\left(40\right)}\\ y=\sqrt{2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 5}\\ y=16\sqrt{5}\end{array}$