The sides of an equilateral triangle are increasing at the rate of `sqrt 3` cm/sec. find the rate at which the area of the triangle is increasing when the side is 4 cm long.

Explanation

Let x be the length of each side of an equilateral triangle :
Given that dx/dt =`sqrt 3` cm/sec. if A is the area of the triangle then
`A = sqrt 3/4 x^2 rArr dA/dt = sqrt 3/4 cdot 2x dx/dt = sqrt 3/2 x cdot dx/dt`
Now dA/dt](x=4) = sqrt 3/2 xx 4xx sqrt 3=6`
therefore Area of the triangle is increasing at the rate of 6 `cm^2/sec`.