Question

The side of an equilateral triangle is increasing at the rate of 2 cm/s. at what rate is its area increasing when the side of the triangle is 20 cm ?

Answer 1

$y = \frac{ \sqrt{3} }{4} {x}^{2} \\ \frac{dy}{dt} = \frac{ \sqrt{3} }{2} (2x)( \frac{dx}{dt} ) \\ \frac{dy}{dt} = \frac{ \sqrt{3} }{2} (2 \times 20)(2) \\ \frac{dy}{dt} = 40\sqrt{3}$
area is increasing by this rate..