Question 1121142
This can be only a way to get started, if you want:

Let 2x be the side length of the equilateral triangle.
Let y be the altitude or height of the equilateral triangle.


{{{system((1/2)xy=9sqrt(3),y^2+x^2=4x^2)}}}


{{{system(xy=9*sqrt(3),y=x*sqrt(3))}}}


{{{highlight_green(x=3)}}} and therefore side of equilateral triangle {{{highlight_green(2x=6)}}}.


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