CAT 2023 Geometry & Mensuration Question (Hard)

Question

In a rectangle ABCD, AB 9 cm and BC 6 cm. P and Q are two points on BC such that the areas of the figures ABP, APQ, and AQCD are in geometric progression. If the area of the figure AQCD is four times the area of triangle ABP, then BP PQ QC is

Accepted Answer

Step 1 Let the rectangle ABCD have - AB 9 cm length - BC 6 cm height Let points P and Q lie on BC such that - BP x - PQ y - QC z So, total height cm We are told that areas of regions ABP, APQ, and AQCD are in geometric progression G.P. Also Area AQCD 4 Area ABP So the three areas are in ratio and So

CAT 2023

Quantitative

Geometry & Mensuration

Hard

In a rectangle ABCD, AB = 9 cm and BC = 6 cm. P and Q are two points on BC such that the areas of the figures ABP, APQ, and AQCD are in geometric progression. If the area of the figure AQCD is four times the area of triangle ABP, then BP : PQ : QC is

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