The question is from the topic triangles. It is about a trapezium inside a triangle.CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems. We have to find the ratio of the area of triangle to the area of trapezium.
Question 42: M and N are two points on the side PQ and PR of a triangle PQR respectively such that MNQR is a trapezium and MN:QR = 2:5. Find the ratio of the area of triangle PMN : Trapezium MNQR.
Given, MNQR is a trapezium => MN || QR
Therefore, ฮPMN ~ ฮPQR
Since, MN:QR = 2:5, heights of ฮPMN and ฮPQR will also be in the ration 2:5.
=> \\frac{AฮPMN}{A โญMNQR}\\) = \\frac{AฮPMN}{(AฮPQR-AฮPMN)}\\)
= \\frac{(1/2) * 2b โ 2h}{(1/2) * 5b โ 5h - (1/2) * 2b โ 2h}\\) = \\frac{4}{25-4}\\) = \\frac{4}{21}\\)
The question is "Find the ratio of the area of triangle PMN : Trapezium MNQR."
Choice C is the correct answer.
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