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