CAT Question Paper Quants Slot 2 - CAT Mensuration Questions, 2IIM CAT 2024 CAT COurse Online, CAT coaching in Chennai

× CAT Questions
CAT Quantitative Aptitude
Geometry HCF and LCM Factors Remainders Factorials Digits Ratios,Mixtures;Averages Percents; Profits; SICI Speed & Time; Races Logarithms and Exponents Pipes,Cisterns; Work,Time Set Theory Coordinate Geometry Mensuration Trigonometry Linear & Quadratic Equations Functions Inequalities Polynomials Progressions Permutation Probability
CAT Verbal
Para Jumble Sentence Correction Sentence Elimination Paragraph Completion Reading Comprehension Critical Reasoning Word Usage Para Summary Text Completion

CAT Online Coaching

CAT Questions

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

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

Video Solution

Explanatory Answer

🎉Republic Day Special: Get up to ₹14,000 OFF on CAT 2026–27 Courses 🇮🇳

2IIM : Best Online CAT Coaching.

Best CAT Online Coaching
Try upto 40 hours for free
Learn from the best!

2IIM : Best Online CAT Coaching.

Video Explanation

Best CAT Coaching in Chennai

CAT Coaching in Chennai - CAT 2022
Limited Seats Available - Register Now!

Explanatory Answer

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"