The sides of an equilateral triangle are increasing at a rate of 10 cm/min. at what rate is the area of the triangle increasing when the sides are 30 cm long?

Area of a triangle is given by



Since the sides of an equilateral triangle are equal.

Differentiating the area of the triangle, we have:



where





Therefore, the rate is the area of the triangle increasing when the sides are 30 cm long is 259.8 cm^2 / min