CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Triangles

CAT Questions

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.

1. 4:25
2. 1:2
3. 4:21
4. 4:10

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Explanatory Answer

Method of solving this CAT Question from Triangles: Properties of similar triangles would be useful.

Given, MNQR is a trapezium => MN || QR
Therefore, ΔPMN ~ ΔPQR
Since, MN:QR = 2:5, heights of ΔPMN and ΔPQR will also be in the ration 2:5.
=> \\frac{AΔPMN}{A ▭MNQR}\\) = \\frac{AΔPMN}{(AΔPQR-AΔPMN)}\\)
= \\frac{(1/2) * 2b ∗ 2h}{(1/2) * 5b ∗ 5h - (1/2) * 2b ∗ 2h}\\) = \\frac{4}{25-4}\\) = \\frac{4}{21}\\)

The question is "Find the ratio of the area of triangle PMN : Trapezium MNQR."

Hence, the answer is 4:21.

Choice C is the correct answer.