Question:
The side of a square is increasing at the rate of $0.2 \mathrm{~cm} / \mathrm{sec}$. Find the rate of increase of the perimeter of the square.
Solution:
Let $x$ be the side and $P$ be the perimeter of the square at any time $t .$ Then,
$P=4 x$
$\Rightarrow \frac{d P}{d t}=4 \frac{d x}{d t}$
$\Rightarrow \frac{d P}{d t}=4 \times 0.2$ $\left[\because \frac{d x}{d t}=0.2 \mathrm{~cm} / \mathrm{sec}\right]$
$\Rightarrow \frac{d P}{d t}=0.8 \mathrm{~cm} / \mathrm{sec}$