CAT 2023 Geometry & Mensuration Question (Hard)

Question

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

Accepted Answer

Step-by-step solution --- Step 1 Given data Right-angled triangle Altitude cm Base cm Area of triangle _ ABC 2 times BC times AB 2 times 12 times 5 30 2 Points and lie on such that areas of , , and are in arithmetic progression A.P. . Also, . --- Step 2 Let the areas Let _ ABP A_1, _ ABQ A_2, _ ABC

CAT 2023

Quantitative

Geometry & Mensuration

Hard

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

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