Question

The figures to the right are similar. Compare the first figure to the second. Give the ratio of the perimetersand the ratio of the areas.

Answer 1

SOLUTION

Since the rectangles are similar,

The ratio of their perimeter is thus

$\begin{gathered} \frac{P1}{P2}=\frac{l1}{l2} \\ \\ \frac{P1}{P2}=\frac{10}{25} \\ \\ P1\colon P2=\frac{2}{5} \\ \\ P1\colon P2=2\colon5 \end{gathered}$

Ratio of their areas become

$\begin{gathered} \frac{A1}{A2}=\lbrack\frac{l1}{l2}\rbrack^2 \\ \\ \frac{A1}{A2}=\lbrack\frac{10}{25}\rbrack^2 \\ \\ \frac{A1}{A2}=\frac{100}{625} \\ \\ \frac{A1}{A2}=\frac{4}{25} \\ \\ A1\colon A2=4\colon25 \end{gathered}$