Given that ABC is a right-angled triangle with AB=5 and BC=12⇒ Area of the triangle =0.5*5*12=30. Let us assume BP=p,BQ=q ⇒ Area of ABP=0.5*5*p=2.5p ⇒ Area of ABQ=0.5*5*q=2.5q Given the area of ABC is 1.5 times that of ABP ⇒30=1.5*2.5p⇒20=2.5p⇒p=8 Given Areas of ABP,ABQ and ABC are in A.P. ⇒2*2.5q=2.5*8+30⇒5q=50⇒q=10. PQ=BQ−BP=q−p=10−8=2.