Side of an equilateral triangle expands at the rate of `2 cm`/`sec`. The rate of increase of its area when each side is `10 cm` is

Explanation

We know that,

`A=frac{sqrt(3)}{4}x^2`

Differentiating both sides w.r.t `t`

`(dA)/(dt)=frac{sqrt(3)}{2}x(dx)/(dt)`


Given that,

`(dx)/(dt)=2, x=10`

`(dA)/(dt)=frac{sqrt(3)}{2}*10*2`

`(dA)/(dt)=10sqrt(3) cm^2`/`sec``