Question

Find the values of the ratios (red to blue) of the perimeters and areas of the similar figures.

Answer 1

Step 1: Find the ratio of perimeter of figures.

Given, figure

From figure, we can have

Side length of red figure $=11$

Side length of blue figure $=6$

Since, we know that when two figures are similar then

$\Rightarrow \frac{PerimeteroffigureA}{PerimeteroffigureB}=\frac{SidelengthoffigureA}{SidelengthoffigureB}$

So, the ratio of perimeter of red figure to the blue figure will be

$$\begin{gathered} \Rightarrow \frac{Perimeterofredfigure}{Perimeterofbluefigure}=\frac{Sidelengthofredfigure}{Sidelengthofbluefigure} \\ \Rightarrow \frac{Perimeterofredfigure}{Perimeterofbluefigure}=\frac{11}{6} \end{gathered}$$

Step 2: Find the ratio of area of figures.

Since, we know that when two figures are similar then

$\Rightarrow \frac{AreaoffigureA}{AreaoffigureB}=\frac{{(SidelengthoffigureA)}^2}{{(SidelengthoffigureB)}^2}$

So, the ratio of area of red figure to the blue figure will be

$$\begin{gathered} \Rightarrow \frac{Areaofredfigure}{Areaofbluefigure}=\frac{{(Sidelengthofredfigure)}^2}{{(Sidelengthofbluefigure)}^2} \\ \Rightarrow \frac{Areaofredfigure}{Areaofbluefigure}=\frac{{11}^2}{6^2}=\frac{121}{36} \end{gathered}$$

Hence, the ratio of perimeter and area of red figure to the blue figure is $\frac{11}{6}$ and $\frac{121}{36}$ respectively.