Question 1151096
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<pre>

Since the length of EC is  {{{3/4}}}  of the length of AD,  the area of the triangle AEC is  {{{3/4}}}  of the area of the triangle ABC.


Thus the area of the triangle ABC  is  {{36*sqrt(3)}}}  cm^2,  or


    {{{a^2*(sqrt(3)/4)}}} = {{{36*sqrt(3)}}}.


Then  {{{a^2}}} = 36*4;  hence,  a = 6*2 = 12 centimeters.    <U>ANSWER</U>
</pre>

Solved.