A) \[\sqrt{3}\,sq\text{ }cm/s\]
B) 10 sq cm/s
C) \[10\sqrt{3}\,sq\text{ }cm/s\]
D) \[\frac{10}{\sqrt{3}}\,sq\text{ }cm/s\]
E) \[10\sqrt{2}\,sq\text{ }cm/s\]
Correct Answer: C
Solution :
Let\[x\]be the side of equilateral triangle. \[\therefore \] Area of equilateral triangle \[A=\frac{\sqrt{3}}{4}{{x}^{2}}\] On differentiating w.r.t. t, we get \[\frac{dA}{dT}=\frac{\sqrt{3}}{4}.2x\frac{dx}{dt}\] Given that\[\frac{dx}{dt}=2cm/s\]and\[x=10\text{ }cm\] \[\therefore \] \[\frac{dA}{dt}=\frac{\sqrt{3}}{4}.20.2=10\sqrt{3}\,sq\,cm/s\]
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