Packing three squares into an equilateral triangle

Question

I am trying to pack 3 equal, largest possible sized squares into an equilateral triangle.

Answer 1

Erich Friedman, a professor in Stetson University got the solution to this as posted in his website.

His solution gives the way to pack tree unit squares in the smallest possible equilateral triangle of side $s$.

The formula for $s$ is easily verified using elementary trigonometry. Why this one is the most optimal configuration I do not know...

Reformulated for our problem, given an equilateral triangle of side $s$, the side $a$ of the biggest 3 equal squares that fit inside is

\begin{equation} a=\frac{s}{\frac{3}{2}+\sqrt{3}} \end{equation}