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 $B$?

   Hint (a):

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

   Answer (a):

   $\frac {4}{25}$

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

   Answer (b):

   $196{:}1$

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

   Hint (c):

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