. CAT 2018 Question Paper Quants Slot 2 - CAT Mensuration Questions, 2IIM CAT 2020 online classes, CAT coaching in Chennai | 2IIM Online CAT Coaching

# CAT 2018 Question Paper | Quants Slot 2

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

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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. ###### Signup and sample 9 full classes for free The Best Online CAT Coaching Courses. Signup ! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2020Enroll at 44,000/- Next Weekend Batch Starts Sun, Feb 23rd, 2020 ###### Best CAT Coaching in ChennaiRegister Online, get Rs 4000/- off Attend a Demo Class ##### 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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