[tex]\bf \textit{Area of an equilateral triangle}\\\\
A=\cfrac{s^2\sqrt{3}}{4}\qquad
\begin{cases}
s=\textit{length of one side}\\
----------\\
A=4\sqrt{3}
\end{cases} \implies 4\sqrt{3}=\cfrac{s^2\sqrt{3}}{4}
\\\\\\
\cfrac{4\cdot 4\sqrt{3}}{\sqrt{3}}=s^2\implies \sqrt{\cfrac{4\cdot 4\sqrt{3}}{\sqrt{3}}}=s
\\\\
-----------------------------\\\\
perimeter=s+s+s=3s\impliedby \textit{since all sides are equal}[/tex]
