A) \[\sqrt{3}c{{m}^{2}}/s\]
B) \[10c{{m}^{2}}/s\]
C) \[10\sqrt{3}c{{m}^{2}}/s\]
D) \[\frac{10}{\sqrt{3}}c{{m}^{2}}/s\]
Correct Answer: C
Solution :
Let \[x\] be the side of and equilateral triangle and A be the area. \[\therefore \] \[A=\frac{\sqrt{3}}{4}{{x}^{2}}\] On differentiating both sides w. r. t. t, we get \[\frac{dA}{dt}=\frac{\sqrt{3}}{4}2x\frac{dx}{dt}\] Given, \[x=10cm\] and \[\frac{dx}{dt}=2cm/s\] \[\therefore \] \[\frac{dA}{dt}=\frac{\sqrt{3}}{4}2\times (10)\times 2\] \[=10\sqrt{3}c{{m}^{2}}/s\]
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