Chapter 11.8, Problem 5ST2

To determine

To Find: The ratio of perimeters.

Answer to Problem 5ST2

  $6:9$

Explanation of Solution

Given: The area of two similar triangles are $36and81$

Ratio of areas

  $\frac{a^2}{b^2}=\frac{36}{81}$

Ratio of perimeters

  $\begin{array}{l}\frac{a^2}{b^2}=\frac{36}{81}\\ \frac{a}{b}=\sqrt{\frac{36}{81}}\\ \frac{a}{b}=\frac{6}{9}\end{array}$

Hence, the ratio of perimeters is $6:9$ .