Question

The area of an equilateral triangle is given by the formula a=sqrt3/4 (s)^2. Which formula represents the length of an equilateral triangle's side (s) in terms of the triangle's area (A)?

Answer 1

$\bf \textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2\sqrt{3}}{4}\qquad s=side's~length \\\\\\ 4A=s^2\sqrt{3}\implies \cfrac{4A}{\sqrt{3}}=s^2\implies \sqrt{\cfrac{4A}{\sqrt{3}}}=s \\\\\\ \stackrel{\textit{and if we rationalize the denominator}}{\sqrt{\cfrac{4A}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}}}\implies \sqrt{\cfrac{4A\sqrt{3}}{3}}}$