# 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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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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