#### Question

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

#### Solution

\[\text { Let x be the side and P be the perimeter of the square at any timet. Then },\]

\[P = 4x\]

\[ \Rightarrow \frac{dP}{dt} = 4\frac{dx}{dt}\]

\[ \Rightarrow \frac{dP}{dt} = 4 \times 0 . 1 \left[ \because\frac{dx}{dt}=0.1 cm/sec \right]\]

\[ \Rightarrow \frac{dP}{dt} = 0 . 4 cm/\sec\]

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Solution The Side of a Square is Increasing at the Rate of 0.1 Cm/Sec. Find the Rate of Increase of Its Perimeter ? Concept: Rate of Change of Bodies Or Quantities.