Chapter 11, Problem 31SGR

To determine

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

Answer to Problem 31SGR

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.

  $\begin{array}{l}\mathrm{Area}ofsimilar\mathrm{figures}=ratiothesquareofcorrespondingsides\\ \frac{8}{32}={\left(\frac{4}{x}\right)}^2\\ \sqrt{\frac{8}{32}}=\frac{4}{x}\\ \sqrt{\frac{1}{4}}=\frac{4}{x}\\ \frac{1}{2}=\frac{4}{x}\\ x=8\end{array}$

The scale factor from the blue to the green figure:

  $\begin{array}{l}=\frac{4}{8}\\ =\frac{1}{2}\end{array}$

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