Question 1105588
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The altitude of an equilateral triangle is also a median.  If AE is a median of triangle ABD, then the base of triangle AEC is 3/4 the side length of the equilateral triangle.<br>
If the area of triangle AEC is {{{27*sqrt(3)}}}, then the area of the equilateral triangle is 4/3 of that, or {{{36*sqrt(3)}}}.<br>
The area of an equilateral triangle is {{{(s^2*sqrt(3))/4}}}, so
{{{(s^2*sqrt(3))/4 = 36*sqrt(3)}}}
{{{s^2 = 144}}}
{{{s = 12}}}<br>
The side length of the equilateral triangle is 12 cm.