CAT 2018 Quant Questions

Question:
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

1:4
2:9
1:3
3:8
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Correct Answer: 1

Let 'a' and 'b' be the length of sides of the rectangle. (a > b)

Area of the rectangle = a*b

Perimeter of the rectangle = 2*(a+b)

\( \Rightarrow \) \(\frac{{a*b}}{{{{(2*(a + b))}^2}}} = \frac{1}{{25}}\)

\( \Rightarrow \) \(25ab = 4{(a + b)^2}\)

\( \Rightarrow \) \(4{a^2} - 17ab + 4{b^2} = 0\)

\( \Rightarrow \) \((4a - b)(a - 4b) = 0\)

\( \Rightarrow \) \(a = 4b\) or \(\frac{b}{4}\)

We initially assumed that a > b, therefore a \( \ne \) \(\frac{b}{4}\).

Hence, a = 4b

\( \Rightarrow \) b : a = 1 : 4

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CAT 2018 Quant Questions
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