Question
The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
Answer: Option C
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Let original length = x metres and original breadth = y metres.
Original area = (xy) m2.
New length = \(\left(\frac{120}{100}x\right)m=\left(\frac{6}{5}x\right)m.\)
New breadth = \(\left(\frac{120}{100}y\right)m=\left(\frac{6}{5}y\right)m.\)
New Area = \(\left(\frac{6}{5}x\times\frac{6}{5}y\right)m^{2}.=\left(\frac{36}{25}xy\right)m^{2}\)
The difference between the original area = xy and new-area 36/25 xy is
= (36/25)xy - xy
= xy(36/25 - 1)
= xy(11/25) or (11/25)xy
So, Increase % = \(\left(\frac{11}{25}xy\times\frac{1}{xy}\times100\right)\) %= 44%
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