Question

The area of a square is increasing at the rate of $0.5$ cm/sec. Find the rate of increase of it's perimeter when the side of the square is $10$cm long.

Answer 1

If x cm. is the side of the square and p cm. is the perimeter.
$p=4x$
$\therefore \frac{dp}{dt}=4\frac{dx}{dt}$
$=4\times 0.5$ $(\because \frac{dx}{dt}=0.5$ given$)$
$=2$
$\therefore$ The perimeter is increasing at the rate of $2$ cm/sec.