Chapter E, Problem 11.15EX

To determine

To find the area of the equilateral triangle having perimeter 24 units.

Answer to Problem 11.15EX

Option (d)

Explanation of Solution

Given information: Perimeter of equilateral triangle 24 units.

Concept used:

  $\begin{array}{l}\text{Area of the equilateral triangle}=\frac{\sqrt{3}}{4}\times a^2\\ \text{Perimeter of the equilateral triangle}=3a\end{array}$

Given,

  $\begin{array}{l}\text{Perimeter of the equilateral triangle}=3a=24\\ \Rightarrow a=8\end{array}$

  $\text{Area of the equilateral triangle}=\frac{\sqrt{3}}{4}\times a^2=\frac{\sqrt{3}}{4}\times 8\times 8=16\sqrt{3}$

Hence, the area of the equilateral traingle is $16\sqrt{3}$ square units.