Cayley Mathematical Olympiad 2005 Q3

In triangle $ABC$, angle $B$ is a right angle and $X$ is the point on $BC$ so that $BX:XC=5:4$. Also, the length of $AB$ is three times the length of $CX$ and the area of triangle $CXA$ is 54cm2.

Calculate the length of the perimeter of triangle $CXA$.