# Problematic Perimeter.. or is it?

Level pending

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 $$\triangle AHG$$ ?

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