The side of an equilateral triangle is increasing at the rate

Question:

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

Solution:

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

$P=3 x$

$\Rightarrow \frac{d P}{d t}=3 \frac{d x}{d t}$

$\Rightarrow \frac{d P}{d t}=3 \times \frac{1}{3}$         $\left[\because \frac{d x}{d t}=\frac{1}{3} \mathrm{~cm} / \mathrm{sec}\right]$

$\Rightarrow \frac{d P}{d t}=1 \mathrm{~cm} / \mathrm{sec}$

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