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

let $A=$area and $a=$side

$A=\frac{\sqrt{3}{a}^2}{4}$

By chain rule:

$\frac{dA}{dt}=\frac{dA}{da}\times \frac{da}{dt}=\frac{\sqrt{3}a}{2}\times \frac{da}{dt}a=20cm,\frac{da}{dt}=2cm/s\Rightarrow \frac{dA}{dt}=20\sqrt{3}{cm}^2/s$