Chapter 15, Problem 12CR

To determine

To Find: The ratio of the perimeter of the two regular pentagons.

Answer to Problem 12CR

  $\frac{2\sqrt{2}}{3\sqrt{2}}$

Explanation of Solution

Given:

  $\text{Two regular pentagons having areas }8\&18.$

Formula Used:

Proportional Area-Perimeter Theorem: It states that if two figures are similar then

  $\frac{\sqrt{Area}}{\sqrt{Area}}=\frac{Perimeter}{perimeter}$ .

Calculation:

  $\begin{array}{l}\text{Two regular pentagons having areas }8\&18.\\ let,\\ \text{ratio of the perimeter be}\frac{a}{b}\\ \frac{a}{b}=\frac{\sqrt{a^2}}{\sqrt{b^2}}\\ \text{⇒}\frac{a}{b}=\frac{\sqrt{8}}{\sqrt{18}}\\ \text{⇒}\frac{a}{b}=\frac{2\sqrt{2}}{3\sqrt{2}}\end{array}$

Conclusion:

Thus the requiredratio of their perimeter is $\frac{2\sqrt{2}}{3\sqrt{2}}$ .