Chapter 11.5, Problem 27HP

To determine

To Prove: The equation relating the perimeter of the enlarged figure to the perimeter of the original Figure Q.

Answer to Problem 27HP

The required equation is $P_{Enlarged}=Q\sqrt{R}$ .

Explanation of Solution

Given:

The ratio of the area of enlarged Figure to the area of the original figure is $R$ .

Calculation:

Consider by the theorem of the similar polygon the scale factor is,

  $\begin{array}{l}{k}^2=R\\ k=\sqrt{R}\end{array}$

Then, the ratio of the perimeter is,

  $\begin{array}{l}\frac{P_{Enlarged}}{P_{original}}=k\\ \frac{P_{Enlarged}}{P_{original}}=\sqrt{R}\\ P_{Enlarged}=Q\sqrt{R}\end{array}$