Question

It's your creative contracting at uniform rate 4 cm square per second then the rate at which perimeter is decreasing when the side of square is 20 CM

Answer 1

The perimeter is decreasing at a rate of -0.4 cm/s.

Answer 2

Given:

$$\frac{dA}{dt} = -4 \ \text{cm}^2/\text{s}, \quad A = s^2, \quad s = 20 \ \text{cm}, \quad P = 4s.$$

Differentiate $A = s^2$ with respect to time:

$$\frac{dA}{dt} = 2s \frac{ds}{dt} \quad \Longrightarrow \quad \frac{ds}{dt} = \frac{\frac{dA}{dt}}{2s} = \frac{-4}{2 \times 20} = -0.1 \ \text{cm/s}.$$

Differentiate the perimeter $P = 4s$:

$$\frac{dP}{dt} = 4 \frac{ds}{dt} = 4(-0.1) = -0.4 \ \text{cm/s}.$$

Explanation: Differentiate area $A = s^2$ to get $s$ rate, then use $P = 4s$ to find the perimeter rate.