# Packing three squares into an equilateral triangle

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

• I wish you luck! (If you decide you'd like some help with that, let us know what you've tried, where you're stuck, and other details like that.) Mar 8, 2013 at 19:17

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
$$a=\frac{s}{\frac{3}{2}+\sqrt{3}}$$