Question

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

Answer 1

$$\begin{gathered} \text{Let}\mathit{\text{x}}\text{be the side and}\mathit{\text{P}}\text{be the perimeter of the square at any time}\mathit{\text{t}}\text{. Then,} \\ P=4x \\ \Rightarrow \frac{dP}{dt}=4\frac{dx}{dt} \\ \Rightarrow \frac{dP}{dt}=4\times 0.1\left[\text{∵}\frac{dx}{dt}\text{=0.1 cm/sec}\right] \\ \Rightarrow \frac{dP}{dt}=0.4\mathrm{cm}/\sec \end{gathered}$$