Chapter 11.5, Problem 26HP

To determine

To Prove: The scale factor that must be multiplied to each of the side.

Answer to Problem 26HP

The required scale factor is $\frac{\sqrt{x}}{100}$ .

Explanation of Solution

Given:

The area of the polygon such that it must be $x\%$ of the original area.

Calculation:

Consider the area of the polygon is $A$ .

Consider the area is $x\%$ of the original area, then the area of the original polygon is,

  $\frac{x}{100}A$

Then, by the area of the similar polygon shows that,

  $\begin{array}{l}{k}^2=\frac{\left(\frac{x}{100}A\right)}{A}\\ k=\frac{\sqrt{x}}{100}\end{array}$

Thus, the required scale factor is $\frac{\sqrt{x}}{100}$ .