The side of a square is increasing at the rate

Question:

The side of a square is increasing at the rate of $0.2 \mathrm{~cm} / \mathrm{sec}$. Find the rate of increase of the perimeter of the square.

Solution:

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

$P=4 x$

$\Rightarrow \frac{d P}{d t}=4 \frac{d x}{d t}$

$\Rightarrow \frac{d P}{d t}=4 \times 0.2$      $\left[\because \frac{d x}{d t}=0.2 \mathrm{~cm} / \mathrm{sec}\right]$

$\Rightarrow \frac{d P}{d t}=0.8 \mathrm{~cm} / \mathrm{sec}$

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