The percentage increase in the area of a rect | vedclass

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(C) Let the initial length be $l$ and the initial breadth be $b$. The initial area is $A_1 = l 	imes b$.If each side is increased by $20 \%$,the new

Vedclass · Accepted Answer

$44$

Vedclass · Answer

(C) Let the initial length be $l$ and the initial breadth be $b$. The initial area is $A_1 = l 	imes b$.If each side is increased by $20 \%$,the new length $l' = l + 0.20l = 1.2l$ and the new breadth $b' = b + 0.20b = 1.2b$.The new area is $A_2 = l' 	imes b' = (1.2l) 	imes (1.2b) = 1.44lb = 1.44A_1$.The percentage increase in area is given by $\frac{A_2 - A_1}{A_1} 	imes 100 = \frac{1.44A_1 - A_1}{A_1} 	imes 100 = 0.44 	imes 100 = 44 \%$.Alternatively,using the formula for successive percentage change: $x + y + \frac{xy}{100} = 20 + 20 + \frac{20 	imes 20}{100} = 40 + 4 = 44 \%$.

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

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