Chapter 11, Problem 32SGR

To determine

To find: The scale factor from the blue to the green figure and find $x$ .

Answer to Problem 32SGR

The scale factor is $\frac{1}{2}$ and the value of $x=8$ .

Explanation of Solution

Given information: Area of two figures are given and side of one figure is given.

Calculation: Area of two figures are given and side of one figure is given.

  $\begin{array}{l}\mathrm{Area}ofsimilar\mathrm{figures}=ratiothesquareofcorrespondingsides\\ \frac{525}{1575}={\left(\frac{x}{18}\right)}^2\\ \sqrt{\frac{525}{1575}}=\frac{x}{18}\\ \sqrt{\frac{1}{3}}=\frac{x}{18}\\ \frac{18}{\sqrt{3}}=x\\ \frac{18}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}=x\\ \frac{18\sqrt{3}}{3}=x\\ 6\sqrt{3}=x\end{array}$

The scale factor from the blue to the green figure:

  $\begin{array}{l}=\frac{6\sqrt{3}}{18}\\ =\frac{\sqrt{3}}{3}\end{array}$

Thus the scale factor is $\frac{\sqrt{3}}{3}$ and the value of $x=6\sqrt{3}$ .