Triangle Area Arithmetic Progression

In a right-angled triangle ∆ABC, the altitude AB is 5 cm, and the base BC  is 12 cm. P and Q are two points on BC such that the areas of ∆ABP,  ∆ABQ and ∆ABC are in arithmetic progression. If the area of ∆ABC is 1.5  times the area of ∆ABP, the length of PQ, in cm, is