Question : The area of a rectangle is thrice that of a square. The length of the rectangle is $20\;\mathrm{cm}$ and the breadth of the rectangle is $\frac{3}{2}$ times that of the side of the square. The side of the square, (in cm) is:
Option 1: 10
Option 2: 20
Option 3: 30
Option 4: 60
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Correct Answer: 10
Solution :
Let the side of the square be $ s\text{ cm}$.
The area of the square $= s^2\;\mathrm{cm^2}$
Given that the area of the rectangle is thrice that of the square.
The area of the rectangle $=3s^2\;\mathrm{cm^2}$ ____(i)
Given that the length of the rectangle is $20\;\mathrm{cm}$ and its breadth is $\frac{3}{2}s\text{ cm}$.
The area of the rectangle $=20 \times \frac{3}{2}s = 30s\;\mathrm{cm^2}$____(ii)
From equation (i) and (ii),
$⇒3s^2 = 30s$
$⇒s = \frac{30}{3} = 10\;\mathrm{cm}$
Hence, the correct answer is 10.
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