SOLUTION
Consider the image below
The ratio of the side is given by
[tex]\begin{gathered} \text{large to small} \\ \frac{\text{large}}{small}=\frac{length\text{ of the side of the large triangle}}{Length\text{ of the side of small triangle }}=\frac{10}{5}=\frac{2}{1} \\ \\ \end{gathered}[/tex]
Since the ratio of the side is the scale factor
[tex]\text{the scale factor =}\frac{2}{1}[/tex]
hence The raio of the perimeters is the scale factor
Therefore
The ratio of their parimeter is 2 : 1
The ratio of the Areas is square of the scale factor
[tex]\text{Ratio of Area =(scale factor )}^2[/tex]
Hence
[tex]\begin{gathered} \text{ Since scale factor=}\frac{2}{1} \\ \text{Ratio of Area=}(\frac{2}{1})^2=\frac{2^2}{1^2}=\frac{4}{1} \\ \text{Hence} \\ \text{Ratio of their areas is 4 : 1} \end{gathered}[/tex]
Therefore
The ratio of their Areas is 4 :1
