Question

Side of an equilateral triangle expands at the rate of $2cm/\sec$. If the rate of increase of its area when each side is $10cm$ is $k\sqrt{3}c{m}^2/\sec$ then find $k$.

Answer 1

Answer: 10.00

$[2]$ If $x$ is a side of equilateral triangle then area
$(A)=\frac{\sqrt{3}}{4}{x}^2$
$\frac{dA}{dt}=\frac{\sqrt{3}}{4}\times 2x\frac{dx}{dt}$
$=\frac{\sqrt{3}}{2}\times 10\times 2$
$=10\sqrt{3}c{m}^2/\sec$