The rate of change of the area of a equilateral triangle with respect to its side when its side = 2 is :

$\frac{\sqrt{3}}{4}$ $\sqrt{3}$ $\frac{\sqrt{3}}{2}$ $2\sqrt{3}$

$\sqrt{3}$

Area of equilateral triangle with side x is A(x) = $\frac{\sqrt{3}}{4}x^2$ so rate of change of A(x) wrt x $= A'(x) = \frac{2\sqrt{3}}{4}x$ at x = 2 $A'(2) = \frac{2\sqrt{3} × 2}{4} = \sqrt{3}$