$$\triangle ABC$$ ~ $$\triangle XYZ$$. The ratio of their perimeters is $$ \frac{11}{5} $$, what is their similarity ratio and the ratio of their areas?

What is the ratio of their areas?

$
\text{ratio of perimeters} = \text{similarity ratio}
\\
\text{similarity ratio} = \frac{11}{5}
\\
\text{ratio of areas} = (\text{similarity ratio})^2
\\
= \Big(\frac{11}{5}\Big)^2
\\
\text{ratio of areas} = \frac{121}{25}
$

Problem 3

$$\triangle ABC$$ ~ $$\triangle XYZ$$. The ratio of their areas is $$ \frac{36}{17} $$, what is their similarity ratio and the ratio of their perimeters?