It is given that
AB=9cm,BC=6cm.
It is also known that the areas of the figures
ABP,APQ, and
AQCD are in geometric progression.
Hence, the area of the ABP, APQ, and AQCD are
k,2k, and
4k respectively.
The ratio of
BP,PQ,QC will be the ratio of the respective triangles. Hence, we can draw a line from point
A to point C.
Let the area of triangle
AQC be
x, which implies the area of triangle
ADC=ADQC−AQC=4k−x, which is equal to the sum of the area of triangle APB, AQP, and ACQ, respectively.
Therefore,
4k−x=3k+x⇒x=Hence the ratio of
BP:PQ:CQ=k:2k:=2:4:1