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CAT 2018 [SLOT 2] Quant Question with Solution 28

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. 1:4
2. 2:9
3. 1:3
4. 3:8
Let the length and the breadth of the rectangle be L and B respectively.
Given that $\frac{\text { Area of rectangle }}{\text { Perimeter }^{2}}=\frac{1}{25} \Rightarrow \frac{L \times B}{(2(L+B))^{2}}=\frac{1}{25}$
$\Rightarrow 25 L B=4 L^{2}+4 B^{2}+8 L B$
$= L^{2}+B^{2}=(17 / 4) L B$
(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 ¼ )
Since B < L, the ratio B : L = 1 : 4

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