# CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Triangles

###### CAT Questions | CAT Geometry Questions | Triangles

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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##### 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. ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2024 Classroom Batches Starting Now! @Gopalapuram ###### Best CAT Coaching in Chennai Introductory offer of 5000/- Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Preparation Online | CAT Geometry questions Videos On YouTube #### Other useful sources for Geometry Question | Geometry Triangles Circles Quadrilaterals Sample Questions ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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