Question

The two figures are similar.

1. Find the value of $x$.
2. Find the values of the ratios (red to blue) of the perimeters and of the areas.

Answer 1

Step 1: Find the value of $\mathrm{x}$.

Given, figures

When two figures are similar, then their corresponding sides are equal.

Using the property similar figures.

$$\begin{gathered} \Rightarrow \frac{x}{10}=\frac{14}{8} \\ \Rightarrow x=17.5 \end{gathered}$$

Step 2: Find the ratio of perimeter of figures.

Using property of similar figures.

$\Rightarrow \frac{PerimeteroffigureA}{PerimeteroffigureB}=\frac{sidelengthoffigureA}{sidelengthoffigureB}$

So, the ratio of perimeter of figure (red to blue) is,

$\Rightarrow \frac{Perimeterofredfigure}{Perimeterofbluefigure}=\frac{14}{8}=\frac{7}{4}$

Step 3: Find the ratio of area of figures.

$\Rightarrow \frac{AreaoffigureA}{AreaoffigureB}={\left(\frac{sidelengthoffigureA}{sidelengthoffigureB}\right)}^2$

So, the ratio of area of figure (red to blue) is,

Hence, the value of $\mathrm{x}$ is $17.5$ and ratio of perimeter and area of figure (red to blue) are $\frac{7}{4}$ and $\frac{49}{16}$ respectively.