If the increase in the side of square is $6 \%$, then the approximate percentage increase in its area ......
If the increase in the side of square is $6 \%$, then the approximate percentage increase in its area ......
- $36 \%$
- $12 \%$
- $3 \%$
- $4 \%$
Solution
Let side of square $=x$
Given, percentage change in side $=6 \%$
$
\frac{d x}{x} \times 100=6 \%
$
We have, $A=x^2$
Differentiate w.r.to ' $x$ '
$
\frac{d A}{d x}=2 x \Rightarrow d A=2 x d x
$
Dividing by $x^2$ on both sides
$
\begin{aligned}
\frac{d A}{x^2} & =2 \cdot \frac{x d x}{x^2} \\
\frac{d A}{A} & =2 \frac{d x}{x}
\end{aligned}
$
$
\left[\because A=x^2\right]
$
Now, multiply by 100
$
\frac{d A}{A} \times 100=2 \times\left(\frac{d x}{x} \times 100\right)
$
$
\begin{aligned}
\text { Percentage change in Area } & =2 \times 6 \% \quad \text { [from Eq. (i)] } \\
& =12 \%
\end{aligned}
$
Hence, option (2) is correct
Asked in: AP EAMCET 2020 (22 Sep Shift 2)
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