Each side of an equilateral triangle is increasing at a rate of √3 cm/min. find the rate at which its area increasing when its edge is 12 cm long

Answer 1

First you need to find the area of an equilateral triangle with side x.

Base = x
Height = (√3)x/2
Area = (√3)x²/4

Thus, the area as a function of side x
A(x)=(√3)x²/4

A'(x) = (√3)x/2

Substitute x=12 cm in A'(x) to get rate of change of area (in cm²)