Side of an equilateral triangle expands at the rate of

SOLUTION

Let x be the side and A be the area of equilateral triangle at time t.
Then.$A=\frac{\sqrt{3}}{4}{x}^2$
$\Rightarrow \frac{dA}{dt}=\frac{\sqrt{3}}{2}x\frac{dx}{dt}\Rightarrow \frac{dA}{dt}=\frac{\sqrt{3}}{2}\times 10\times 2=10\sqrt{3}[\because x=10and\frac{dx}{dt}=2]$
Hence (b) is the correct answer.