# 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 \(\triangle AHG\) ?