Question 140
Let $\triangle ABC$ be a right triangle with right angle at $B$. Let the points $D$, $E$, and $F$ be on $AB$, $BC$, and $CA$, respectively, such that $\triangle DEF$ is an equilateral triangle and $EC = FC$. If $DB = 5\sqrt{3}$, $BE = 3$, and $\sin \angle ACB = 4\sqrt{3}/7$, find the perimeter of $\triangle ADF$.