Question

The side of an equilateral triangle is '$a$' units and is increasing at the rate of $\lambda$ units /sec. The rate of increase of its area is

• A. $\frac{2}{\sqrt{3}}\lambda a$
• B. $\sqrt{3}\lambda a$
• C. $\frac{\sqrt{3}}{2}\lambda a$
• D. none of these

Answer 1

Answer: (C)

$\frac{\sqrt{3}}{2}\lambda a$

Given $\frac{da}{dt}=\lambda$
Area of equilateral triangle $A=\frac{\sqrt{3}}{4}{a}^2$
$\Rightarrow \frac{dA}{dt}=\frac{\sqrt{3}}{2}a\frac{da}{dt}$
$\Rightarrow \frac{dA}{dt}=\frac{\sqrt{3}}{2}a\lambda sq.units/sec$