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√(3)}{2}\quad \begin{cases} s=\textit{length of a side}\\ ---------\\ h=36 \end{cases}\implies 36=\cfrac{s√(3)}{2} \\\\\\ 72=s√(3)\implies \cfrac{72}{√(3)}=s~~\stackrel{rationalizing~it}{\implies }~~\cfrac{72}{√(3)}\cdot \cfrac{√(3)}{√(3)}\implies \cfrac{7√(3)}{3}`