The side of a square is increasing at the rate of 0.1 cm/sec. Find the rate of increase of its perimeter
Question:

The side of a square is increasing at the rate of 0.1 cm/sec. Find the rate of increase of its perimeter

Solution:

Let x be the side and P be the perimeter of the square at any time t. Then,

$P=4 x$

$\Rightarrow \frac{d P}{d t}=4 \frac{d x}{d t}$

$\Rightarrow \frac{d P}{d t}=4 \times 0.1$                       $\left[\because \frac{d x}{d t}=0.1 \mathrm{~cm} / \mathrm{sec}\right]$

$\Rightarrow \frac{d P}{d t}=0.4 \mathrm{~cm} / \mathrm{sec}$