Chapter 8.1, Problem 3ACYP

To determine

The value of x, y and z.

Answer to Problem 3ACYP

  $\begin{array}{l}x=2\sqrt{66}\\ y=5\sqrt{33}\\ z=10\sqrt{2}\end{array}$

Explanation of Solution

Given:

  

Calculation:

According to Geometric Mean Altitude Theorem,

  $\begin{array}{l}z=\sqrt{8\left(25\right)}\\ z=\sqrt{200}\\ z=\sqrt{2\times 2\times 2\times 5\times 5}\\ z=10\sqrt{2}\end{array}$

According to Geometric Mean Leg Theorem,

  $\begin{array}{l}x=\sqrt{8\left(8+25\right)}\\ x=\sqrt{8\left(33\right)}\\ x=\sqrt{264}\\ x=\sqrt{2\times 2\times 2\times 3\times 11}\\ x=2\sqrt{66}\\ \text{and}\\ y=\sqrt{25\left(8+25\right)}\\ y=\sqrt{25\left(33\right)}\\ y=\sqrt{5\times 5\times 3\times 11}\\ y=5\sqrt{33}\end{array}$