Problematic Perimeter.. or is it?

In an acute angled $\triangle ABC$ , $AD$ , $BE$ and $CF$ are the altitudes from $A$ , $B$ and $C$ to the sides $BC$ , $AC$ and $AB$ respectively . $BX$ is perpendicular to $FD$ and $CY$ is perpendicular to $DE$ . $BX$ and $CY$ meet at $G$ . If $\angle A$ = $60^\circ$ , $BC$ = $5\sqrt{3}$ cm and $HD$ = $2.4$ cm where $H$ is the orthocentre , what is the perimeter of $\triangle AHG$ ?