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1. The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:

A. 40%

B. 42%

C. 44%

D. 46%

Solution:

Let original length = x metres and original breadth = y metres

\begin{aligned} Original are = (x y) m^{2} \\ New length = (\frac{120}{100} x) m = (\frac{6}{5} x) m \\ New breadth = (\frac{120}{100} y) m = (\frac{6}{5} y) m \\ New area = (\frac{6}{5} x \times \frac{6}{5} y) m^{2} = (\frac{36}{25} x y) m^{2} \\ The difference between the original area = x y \\ and new area \frac{36}{25} x y is \\ = (\frac{36}{25}) x y - x y \\ = x y (\frac{36}{25} - 1) \\ = x y (\frac{11}{25}) o r (\frac{11}{25}) x y \\ ∴ Increase % \\ = (\frac{11}{25} x y \times \frac{1}{x y} \times 100) % \\ = 44 % \end{aligned}

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