Question

An equilateral triangle has an altitude length of 36 feet. Determine the length of a side of the triangle.

Answer 1

$\bf \textit{height of an equilateral triangle}\\\\ h=\cfrac{s\sqrt{3}}{2}\quad \begin{cases} s=\textit{length of a side}\\ ---------\\ h=36 \end{cases}\implies 36=\cfrac{s\sqrt{3}}{2} \\\\\\ 72=s\sqrt{3}\implies \cfrac{72}{\sqrt{3}}=s~~\stackrel{rationalizing~it}{\implies }~~\cfrac{72}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}}\implies \cfrac{7\sqrt{3}}{3}$