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Question
The side of a square is increasing at the rate of 0.1 cm/sec. Find the rate of increase of its perimeter ?
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Solution
\[\text { Let x be the side and P be the perimeter of the square at any time t. Then },\]
\[P = 4x\]
\[ \Rightarrow \frac{dP}{dt} = 4\frac{dx}{dt}\]
\[ \Rightarrow \frac{dP}{dt} = 4 \times 0 . 1 \left[ \because\frac{dx}{dt}=0.1 cm/sec \right]\]
\[ \Rightarrow \frac{dP}{dt} = 0 . 4 cm/\sec\]
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