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 = T^{2}. 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

- 27
- 18
- 21
- 24

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Sides of the rectangle are in the ratio 1 : 3

Take as x and 3x

Area of Rectangle = 3x^{2} = R

Take an equilateral triangle with side a

Area = \\frac{√3}{4}) × a^{2} = T

Given R = T^{2}

3x^{2}= \\frac{√3}{4}) × a^{2}

Solving we get a^{2} = 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 a^{2} = 4x

6^{2} = 4(9)

It works, hence longer side of rectangle is 27

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