Question 53
$ABC$ is an equilateral triangle. $D$ is the midpoint of $BC$, $E$ is a point on $AC$ between $A$ and $C$ and $F$ is a point on $AB$ between $A$ and $B$. The area of $\triangle EDC$ is $24\sqrt{3}$, the area of $\triangle AFE$ is $24\sqrt{3}$ and the area of $\triangle FBD$ is $54\sqrt{3}$. Find the length of the sides of the triangle $ABC$.