Question

Area of an equilateral triangle is given by $A=\dfrac{\sqrt{3}{{a}^{2}}}{4}$, where A is the area and a is the side. Find the perimeter of the triangle if $A=16\sqrt{3}sq.cm.$

Answer 1

Hint: Assume the length of the sides of the triangle to be $x$. Solve the equation hence found using the formula given. Find the perimeter using perimeter = $3x$.

Complete Step-by-step answer:
Given, area of an equilateral triangle $\left( A \right)=\dfrac{\sqrt{3}{{a}^{2}}}{4}$ where a is the length of a side of the length.

Given, $A=16\sqrt{3}sq.cm.$
Let us assume the side of the given triangle to be $x$. Then according to the formula,
$\begin{align}
  & \dfrac{\sqrt{3}{{x}^{2}}}{4}=16\sqrt{3} \\
 & \Rightarrow {{x}^{2}}=64 \\
 & \Rightarrow x=\pm 8 \\
\end{align}$
But, $x$ is the value of length. Therefore, it cannot be negative.
$\therefore x=8$
We know that, perimeter of a triangle is 3 times the length of its sides.
$\therefore $perimeter = 3 x 8 cm
= 24cm
Answer is 24 cm.

Note: While doing calculations involving units, make sure that the uniformity of units is maintained. Also, while mentioning dimension, make sure to write the units also, as any dimension without units is meaningless.