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Question
Side of an equilateral triangle expands at the rate of 2 cm/sec. The rate of increase of its area when each side is 10 cm is
Options
\[10\sqrt{2} \ {cm}^2 /\sec\]
\[10\sqrt{3} {cm}^2 /\sec\]
10 cm2/sec
5 cm2/sec
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Solution
\[10\sqrt{3} \ {cm}^2 /\sec\]
\[\text { Letxbe the side andAbe the area of the equilateral triangle at any timet.Then },\]
\[A = \frac{\sqrt{3}}{4} x^2 \]
\[ \Rightarrow \frac{dA}{dt} = 2 \times \frac{\sqrt{3}}{4} x^{} \frac{dx}{dt}\]
\[\Rightarrow\frac{dA}{dt}=\frac{\sqrt{3}}{2}\times2\times10\]
\[\Rightarrow\frac{dA}{dt}=10\sqrt{3} \ {cm}^2 /sec\]
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