Question

The sides of an equilateral triangle are increasing at the rate of $2cm/sec$. The rate at which the area increases, when side is $10cm$ is

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

Answer 1

Answer: (C)

Area of Equilateral triangle, $A=\frac{\sqrt{3}}{4}{x}^2$
$\frac{dx}{dt}=2cm/s,x=10cm$
$\frac{dA}{dt}=\frac{\sqrt{3}}{4}2x\frac{dx}{dt}$
$=\frac{\sqrt{3}}{4}(20)\cdot 2$
$=10\sqrt{3}c{m}^2/s$