Question

The side of an equilateral triangle is increasing at the rate of $\frac{1}{3}$ cm/sec. Find the rate of increase of its perimeter.

Answer 1

$$\begin{gathered} \text{Let}\mathit{\text{x}}\text{be the side and}\mathit{\text{P}}\text{be the perimeter of the equilateral triangle at any time}\mathit{\text{t.}}\text{Then,} \\ P=3x \\ \Rightarrow \frac{dP}{dt}=3\frac{dx}{dt} \\ \Rightarrow \frac{dP}{dt}=3\times \frac{1}{3}\left[\because \frac{dx}{dt}=\frac{1}{3}\mathrm{cm}/\sec \right] \\ \Rightarrow \frac{dP}{dt}=1\mathrm{cm}/\sec \end{gathered}$$