Question

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

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

Answer 1

The correct option is B

$10\sqrt{3}c{m}^3/sec$

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.