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

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

Solution:

It is given that $\frac{d a}{d t} = λ$

Let A be the area of the triangle. Then,

$\begin{array}{l} A = \frac{\sqrt{3}}{4} a^{2} \\ \Rightarrow \frac{d A}{d t} = \frac{\sqrt{3}}{2} a \frac{d a}{d t} = \frac{\sqrt{3}}{2} a λ \end{array}$

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

Solution:

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