If the increase in the side of a square is 6 | vedclass

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(B) Let the side of the square be $x$. Given that the percentage change in the side is $6 \%$,so $\frac{dx}{x} 	imes 100 = 6 \%$. The area of the squ

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(B) Let the side of the square be $x$. Given that the percentage change in the side is $6 \%$,so $\frac{dx}{x} 	imes 100 = 6 \%$. The area of the square is $A = x^2$. Differentiating with respect to $x$,we get $\frac{dA}{dx} = 2x$,which implies $dA = 2x \, dx$. Dividing both sides by $A = x^2$,we get $\frac{dA}{A} = \frac{2x \, dx}{x^2} = 2 \frac{dx}{x}$. To find the percentage change in area,multiply by $100$: $\frac{dA}{A} 	imes 100 = 2 	imes \left( \frac{dx}{x} 	imes 100 ight)$. Substituting the given value,we get $	ext{Percentage change in Area} = 2 	imes 6 \% = 12 \%$. Thus,the approximate percentage increase in the area is $12 \%$. Therefore,option $B$ is correct.

If the increase in the side of a square is $6 \%$,then the approximate percentage increase in its area is: (in $\%$)

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