Find the perimeter..... Can you??

$\triangle ABC$ is an acute angled triangle. $AD \perp BC, BE \perp AC, CF \perp AB$ and the altitudes are concurrent at $H$ , the orthocenter . $D$ is on BC , $E$ on $AC$ and $F$ on $AB$ . $BX \perp DF$ and $CY \perp DE$ . They meet at $G$ . If $HD = 2.4 cm$ , $BC = 5\sqrt{3}$ and $\angle A = 60^{\circ}$ , find the perimeter of $\triangle AGH$