In a right-angled triangle $\triangle A B C$, the altitude $A B$ is $5 \mathrm{~cm}$, and the base $B C$ is $12 \mathrm{~cm} . P$ and $Q$ are two points on $B C$ such that the areas of $\triangle A B P, \triangle A B Q$ and $\triangle A B C$ are in arithmetic progression. If the area of $\triangle A B C$ is $1.5$ times the area of $\triangle A B P$, the length of $P Q$, in $\mathrm{cm}$, is