Question

if the scale factor between two circles is $\frac{7a}{9b}$ what is the ratio of their areas?
$\frac{49a}{81b}$
$\frac{49a^{2}}{81b^{2}}$
$\frac{81b^{2}}{49a^{2}}$
$\frac{81b}{49a}$

Explanation:

Step1: Recall area - ratio formula

The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding linear measures (scale - factor). If the scale - factor of two circles is $k=\frac{7a}{9b}$, then the ratio of their areas $A_1$ and $A_2$ is $k^{2}$.

Step2: Square the scale - factor

$k^{2}=(\frac{7a}{9b})^{2}=\frac{(7a)^{2}}{(9b)^{2}}=\frac{49a^{2}}{81b^{2}}$

Answer:

$\frac{49a^{2}}{81b^{2}}$