Question

The perimeter of regular polygon having one of its exterior angle as ${72}^o$ is $30$ cm. What is the length of side of equilateral triangle whose perimeter is equal to the length of one side of the polygon?

• A. $6$ cm
• B. $3$ cm
• C. $2$ cm
• D. Cannot be determined.

Answer 1

The correct option is C $2$ cm

Let the number of sides of the polygon be $n$.
Hence, number of exterior angles of the regular polygon will be also $n$.

Given that one exterior angle is ${72}^o$
Hence, sum of all exterior angles of the regular polygon will be $n\times {72}^o$ because all exterior angles of a regular polygon are equal in measure.

We know that sum of all exterior angles of a polygon is ${360}^o$

So, $n\times {72}^o={360}^o\Rightarrow n=\frac{{360}^o}{{72}^0}\Rightarrow n=5$

Hence, the regular polygon is a regular pentagon
Given: It has perimeter $30$ cm.
Because all sides of a regular polygon are equal, let length of each side of pentagon be $x$.
Now, $\text{perimeter}=5x$
$30=5x\Rightarrow x=\frac{30}{5}=6\text{cm}$


Now, let the equilateral triangle have the side $y$.
We know perimeter of triangle=$3y$
Given: Perimeter of the equilateral triangle is equal to side length of the regular pentagon which is $6$ cm.
So, $6=3y\Rightarrow y=\frac{6}{3}=2\text{cm}$


so, option $\left(c\right)$ correct.