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CAT 2020 Question Paper | Quants Slot 2

CAT Previous Year Paper | CAT Quants Questions | Question 16

Irrespective of the time since you've been preparing for the upcoming CAT exam and the time you devote to your online CAT preparation everyday, your preparation will be incomplete without practicing CAT previous year paper. These set you up for the type of questions and their difficulty levels that you can expect in the CAT Question Paper and hence are extermely essential. Start solving questions from CAT Previous Year Paper right away with this Geometry question from CAT 2020 Question paper- Slot 2.
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Question 16 : The sum of perimeters of an equilateral triangle and a rectanmgle is 90 cm. The area, T, of the triangle and the area , R, of the rectangle, both in sq cm, satisfy the relationship R = T2. If the sides of the rectangle are in the ratio 1 : 3, then the length, in cm, of the longer side of the rectangle, is

  1. 27
  2. 18
  3. 21
  4. 24

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Explanatory Answer

Sides of the rectangle are in the ratio 1 : 3
Take as x and 3x
Area of Rectangle = 3x2 = R
Take an equilateral triangle with side a
Area = \\frac{√3}{4}) × a2 = T
Given R = T2
3x2= \\frac{√3}{4}) × a2
Solving we get a2 = 4x
Now from the options longer side 3x = 27
x = 9. Sides of the rectangle are 9 and 27.
If x = 9, Then a = 6
Checking if a2 = 4x
62 = 4(9)
It works, hence longer side of rectangle is 27

The answer is, "27"

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