Chapter 8.1, Problem 35WE

To determine

Find x , y , and z .

Answer to Problem 35WE

  $x=\frac{27}{5}$

  $y=\frac{48}{5}$

  $z=\frac{36}{5}$

Explanation of Solution

Given:

  

Calculation:

The small right triangle with base x is similar to the large right triangle.

So,

  $\begin{array}{l}\frac{9}{15}=\frac{x}{9}\\ \Rightarrow 9^2=15x\mathrm{...................}[\text{multiply each side by 15}\cdot \text{9]}\\ \Rightarrow x=\frac{81}{15}\mathrm{.....................}[\text{divide each side by 15]}\\ \Rightarrow x=\frac{27}{5}\end{array}$

  $\begin{array}{l}x+y=15\\ \Rightarrow y=15-x\mathrm{................}[\text{subtract x from each side]}\\ \Rightarrow y=15-\frac{27}{5}\\ \Rightarrow y=\frac{48}{5}\end{array}$

z is the geometric mean of x and y :

  $\begin{array}{l}z=\sqrt{x\cdot y}\\ \Rightarrow z=\sqrt{\frac{27}{5}\cdot \frac{48}{5}}\\ \Rightarrow z=\frac{36}{5}\end{array}$

So,

  $x=\frac{27}{5}$

  $y=\frac{48}{5}$

  $z=\frac{36}{5}$