CAT 2018 Question Paper Shift 2 Solved Paper

Question : 82 of 100

Marks: +1, -0

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
Options

Validate

Solution:

Let the length and the breadth of the rectangle be

L

and

B

respectively.
Given that

\;{\;\text " Area of rectangle "\;}/{\;\text " Perimeter "\;^{2}}=\;{1}/{25} ⇒ \;{L × B}/{(2(L+B))^{2}}=\;{1}/{25}

⇒ 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

1 {/} 4)

Since

{B}< {L},

the ratio

{B}: {L}=1: 4

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