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

Since the rectangles are similar,

The ratio of their perimeter is thus

`\begin{gathered} (P1)/(P2)=(l1)/(l2) \\ \\ (P1)/(P2)=(10)/(25) \\ \\ P1\colon P2=(2)/(5) \\ \\ P1\colon P2=2\colon5 \end{gathered}`

Ratio of their areas become

`\begin{gathered} (A1)/(A2)=\lbrack(l1)/(l2)\rbrack^2 \\ \\ (A1)/(A2)=\lbrack(10)/(25)\rbrack^2 \\ \\ (A1)/(A2)=(100)/(625) \\ \\ (A1)/(A2)=(4)/(25) \\ \\ A1\colon A2=4\colon25 \end{gathered}`