Question

Side of an equilateral triangle expands at the rate of $2cm/sec$. The rate of increase of its area when each side is $10cm$ is

• A. $10\sqrt{2}c{m}^2/sec$
• B. $10\sqrt{3}c{m}^2/sec$
• C. $10c{m}^2/sec$
• D. $5c{m}^2/sec$

Answer 1

The correct option is B $10\sqrt{3}c{m}^2/sec$

Given $\frac{dx}{dt}=2cm/sec,x=10cm$

$A=\frac{\sqrt{3}}{4}{x}^2$

$\Rightarrow \frac{dA}{dt}=\frac{\sqrt{3}}{2}x\frac{dx}{dt}$

$\Rightarrow \frac{dA}{dt}=10\sqrt{3}c{m}^2/sec$