Each side of a square is increasing at a rate of 2 cm/s. at what rate is the area of the square increasing when the area of the square is 9 cm2?

Let x(t) =  the length of a side of the square (cm) at time t (s).
The rate of change of x is given as


The area (cm²) at time t is 
A = x²

The rate of change of the area with respect to time is


When A = 9 cm², then x = √9 = 3cm. Hence obtain


12 cm²/s