Step-by-step explanation:
Area = Length x Width
A = LW
Differentiating with respect to time
[tex]\frac{dA}{dt}=L\frac{dW}{dt}+W\frac{dL}{dt}[/tex]
Length, L = 20 cm
Width, W = 10 cm
[tex]\frac{dW}{dt}=3cm/s\\\\\frac{dL}{dt}=8cm/s[/tex]
Substituting
[tex]\frac{dA}{dt}=20\times 3+10\times 8\\\\\frac{dA}{dt}=60+80\\\\\frac{dA}{dt}=140cm^2/s[/tex]
Area of rectangle is increasing at 140 cm²/s when the length is 20 cm and the width is 10 cm.
