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

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. 
