Chapter 13.5, Problem 40HP

To determine

To find: Perimeter of the figure.

Answer to Problem 40HP

Perimeter of the given figure is $36$

Explanation of Solution

Given information:

Two sides of a triangle are $12$ and $12$

Angle opposite to one of the $12$ is ${60}^0$

As, Angle opposite to one of the $12$ is ${60}^0$

So, as second side is also $12$ then its opposite angle will also be ${60}^0$

We know

Sum of angles of a triangle is ${180}^0$

Using that

We get

  ${60}^0+{60}^0+x={180}^0$

On solving

We get

  $\begin{array}{l}\Rightarrow {120}^0+x={180}^0\\ \Rightarrow x={180}^0-{120}^0\\ \Rightarrow x={60}^0\end{array}$

As the third angle is also ${60}^0$

So, the length of the remaining third side is also $12$

Therefore,

Perimeter of the given figure is $12+12+12=36$