Chapter 8.1, Problem 3BCYP

To determine

The value of x, y and z.

Answer to Problem 3BCYP

  $\begin{array}{l}x=16\\ y=20\\ z=15\end{array}$

Explanation of Solution

Given:

  

Calculation:

According to Geometric Mean Altitude Theorem,

  $\begin{array}{l}12=\sqrt{x\left(9\right)}\\ 144=9x\\ x=\frac{144}{9}\\ x=16\end{array}$

According to Geometric Mean Leg Theorem,

  $\begin{array}{l}y=\sqrt{16\left(16+9\right)}\\ y=\sqrt{16\left(25\right)}\\ y=\sqrt{4\times 4\times 5\times 5}\\ y=20\\ \text{and}\\ z=\sqrt{9\left(16+9\right)}\\ z=\sqrt{9\left(25\right)}\\ z=\sqrt{3\times 3\times 5\times 5}\\ z=15\end{array}$