Question

The pair of figures to the right are similar. What is the ratio of the perimeters and the ratio of the areas?The ratio of the perimeters is (Simplify your answer.)The ratio of the areas is 1. (Simplify your answer.)

Answer 1

As per given by the question,

There are given that two similar figure.

Now,

From the the figure,

First find the perimeters of the both figure.

So,

From the formula of perimeters of the square,

`P=\text{Sum of all sides}`

Then,

The ratiio of the perieters of the both figure is,

`\begin{gathered} P=\frac{\text{Sum of all side in figure 1}}{Sum\text{ of all side in figure 2}} \\ =(9+9+9+9)/(15+15+15+15) \end{gathered}`

Then,

`\begin{gathered} P=(9+9+9+9)/(15+15+15+15) \\ =(36)/(60) \\ =(3)/(5) \end{gathered}`

Now,

From the formula of the area of the given figure.

`A=(side)^2`

Then,

The ratiao of the area of the given figure is,

`\begin{gathered} A=((sideoffigure1)^2)/((sideoffigure2)^2) \\ A=((9)^2)/((15)^2) \end{gathered}`

Then,

`\begin{gathered} A=((9)^2)/((15)^2) \\ =(81)/(225) \\ =(9)/(25) \end{gathered}`

Hence, the ratio of the perimeters of the given figure is 3/5, and the ratio of the area of the of given figure is 9/25.