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# CAT 2018 Question Paper | Quants Slot 2

###### CAT Previous Year Paper | CAT Mensuration Questions | Question 12

Yet another classic question from Geometry which is pretty doable if you get your equations right. This question was rolled out in CAT Previous Year paper 2018, which can prove to be a motivating factor while you are going through a series of difficult questions. Try this question before having a look at the solution provided. Solve more such questions to ace your online CAT preparation. Visit 2IIM's CAT Question Bank for more such questions.

Question 12 : The area of a rectangle and the square of its perimeter are in the ratio 1 : 25. Then the lengths of the shorter and longer sides of the rectangle are in the ratio

1. 3 : 8
2. 2 : 9
3. 1 : 4
4. 1 : 3

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##### Method of solving this CAT Question from Mensuration

Given that the area of a rectangle and the square of its perimeter are in the ratio 1: 25, we have to find the ratio of the lengths of the shorter and longer sides of the rectangle i.e. b : l
The area of the rectangle = lb
The square of its perimeter = [2(l + b)]2
⟹ lb : [2(l + b)]2 = 1 : 25
⟹ lb : 4[l2 + 2lb + b2] = 1 : 25
⟹ 25 lb = 4[l2 + 2lb + b2]
⟹ 25 lb = 4l2 + 8lb + 4b2
⟹ 4l2 - 17lb + 4b2 = 0
⟹ 4l2 - 16lb - lb + 4b2 = 0
⟹ 4l[l- 4b] – b [l- 4b] = 0
⟹ [l - 4b][4l - b] = 0
By this we can find that the ratio of the shorter and longer sides of the rectangle b : l is in the ratio 1: 4

In other way ,if we want to deal with only one variable and do not want to factorize divide this 4l2 - 17lb + 4b2 = 0 by l2 throughout
⟹ $$frac{4l^2}{l^2}$ - $\frac{17lb}{l^2}$ + $\frac{4b^2}{l^2}$ ⟹ 4 - $\frac{17b}{l}$ + 4[$\frac{b}{l}$]2 Since we have to find ratio of b : l, $\frac{b}{l}$ can be substituted with x 4 - 17x + 4x2 = 0 Now x can be found by simplifying it The question is "The area of a rectangle and the square of its perimeter are in the ratio 1 : 25. Then the lengths of the shorter and longer sides of the rectangle are in the ratio" ##### Hence, the answer is 1 : 4 Choice C is the correct answer. ###### Prepare for CAT 2023 with 2IIM's Daily Preparation Schedule ###### Know all about CAT Exam Syllabus and what to expect in CAT ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2023 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! ##### 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? Mobile:$91) 99626 48484 / 94459 38484
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