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

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    $\begingroup$ 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.) $\endgroup$ – Greg Martin Mar 8 '13 at 19:17
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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 $s$.

Friedman's solution

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}

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  • $\begingroup$ Note, that the web-page says 'smallest known' triangles, so it's most likely not optimal solution $\endgroup$ – Yuriy S Jul 10 '16 at 19:45

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