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

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\(\triangle ABC\) 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 \(\triangle AGH\)

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