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Given the area of an equilateral triangle, what is an algorithm to determine the length of a side?

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    If $A = C\cdot s^2$, then $s=\sqrt{\frac{1}{C}\cdot A}$.2012-11-27

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Let $s$ be the side, and $A$ the area. Drop a perpendicular from one vertex to the opposite side. By the Pythagorean Theorem, the height of the triangle is $\sqrt{s^2-\frac{1}{4}s^2}=\frac{s\sqrt{3}}{2}$. It follows that $A=\frac{s^2\sqrt{3}}{4}.$ Thus $s^2=\frac{4A}{\sqrt{3}},$ and therefore $s=\sqrt{\frac{4A}{\sqrt{3}}}.$ There are several ways to rewrite the above expression.