CAT 2018 Quant Questions

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

Show Answer
Correct Answer: 1
Let the length and the breadth of the rectangle be L and B respectively.
Given that $\frac{\text { Area of rectangle }}{\text { Perimeter }^{2}}=\frac{1}{25} \Rightarrow \frac{L \times B}{(2(L+B))^{2}}=\frac{1}{25}$
$\Rightarrow 25 L B=4 L^{2}+4 B^{2}+8 L B$
$= L^{2}+B^{2}=(17 / 4) L B$
(Note: Alternatively, we can also solve the quadratic equation in terms of L/B and we’d get the same result, i.e. 4 or ¼ )
Since B < L, the ratio B : L = 1 : 4

Get one day FREE Trial of CAT online Full course FREE Registration
Also Check: 841+ CAT Quant Questions with Solutions

CAT Quant Online Course

  • 1000+ Practice Problems
  • Detailed Theory of Every Topics
  • Online Live Sessions for Doubt Clearing
  • All Problems with Video Solutions
₹ 2999

CAT 2018 Questions Paper with Solution PDF Download

CAT 2018 Quant Questions with Solutions

CAT 2018 Slot-1

CAT 2018 Slot-2

Back to Main Page

CAT 2018 Quant Questions
4.9 (97%) 20 vote[s]