The rate of change of the area of a equilateral triangle with respect to its side when its side = 2 is :
Answer & explanation
Correct answer: option 2
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
$A'(2) = \frac{2\sqrt{3} × 2}{4} = \sqrt{3}$