Math Problem (Level 2) : Partition of trapezoid to be triangle (JJ47)

As for trapezoid ABCD in a figure, AD and BC are parallel and AD = 6 cm, BC = 9 cm. 

When point P was set on the side AB, the area ratio of the triangle PCD and trapezoid ABCD was 5 : 9. 

Answer the following questions.

(1) The intersection of the straight line passing along the point P and being parallel to AD and the side CD is set to Q. 

Find the length of PQ.

(2) Find AP : PB by the ratio of the least integer.

Answer

(1) 25/3 cm
(2) 7 : 2

Reference