Question

Referring to the figure, the polygons shown are similar. Findthe ratio (large to small) of their perimeters and areas.

Answer 1

Consider the image below

The ratio of the side is given by

`\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 }}=(10)/(5)=(2)/(1) \\ \\ \end{gathered}`

Since the ratio of the side is the scale factor

`\text{the scale factor =}(2)/(1)`

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

`\text{Ratio of Area =(scale factor )}^2`

Hence

`\begin{gathered} \text{ Since scale factor=}(2)/(1) \\ \text{Ratio of Area=}((2)/(1))^2=(2^2)/(1^2)=(4)/(1) \\ \text{Hence} \\ \text{Ratio of their areas is 4 : 1} \end{gathered}`

Therefore

The ratio of their Areas is 4 :1