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 [tex] \frac{dx}{dt} =2 \, \frac{cm}{s} [/tex]
The area (cm²) at time t is A = x²
The rate of change of the area with respect to time is [tex] \frac{dA}{dt} = \frac{dA}{dx} \frac{dx}{dt} =2 \frac{dA}{dx} =2(2x)=4x \, \frac{cm^{2}}{s} [/tex]
When A = 9 cm², then x = √9 = 3cm. Hence obtain [tex] \frac{dA}{dt} = 4(3) = 12 \, \frac{cm^{2}}{s} [/tex]
