The side of a square sheet is increasing at the rate

Given : $A=x^{2}$ and $\frac{d x}{d t}=4 \mathrm{~cm} / \mathrm{min}$

Let $x$ be the side of the square and $A$ be its area at any time $t .$ Then,

$A=x^{2}$

$\Rightarrow \frac{d A}{d t}=2 x \frac{d x}{d t}$

$\Rightarrow \frac{d A}{d t}=2 \times 8 \times 4$            $\left[\because x=8 \mathrm{~cm}\right.$ and $\left.\frac{d x}{d t}=4 \mathrm{~cm} / \min \right]$

$\Rightarrow \frac{d A}{d t}=64 \mathrm{~cm}^{2} / \min$