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

1 answer:

3 0

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

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