Home > CCG > Chapter 9 > Lesson 9.1.1 > Problem9-8

9-8.

Assume that two figures on a flat surface, $A$ and $B$, are similar.

1. If the linear scale factor is $\frac { 2 } { 5 }$, then what is the ratio of the areas of $A$ and $B$?

$\text{Ratio of areas}=(\text{linear scale factor})^2$

$\frac {4}{25}$

2. If the ratio of the perimeters of $A$ and $B$ is $14{:}1$, what is the ratio of the areas?

$196{:}1$

3. If the area of $A$ is $81$ times that of $B$, what is the ratio of the perimeters?

The ratio of the perimeters is the square root of the ratio of the areas.