Question

The length of a rectangle is increasing at a rate of 4 cm/s and its width is increasing at a rate of 5 cm/s. When the length is 11 cm and the width is 4 cm, how fast is the area of the rectangle increasing?

Answer 1

Related rates:
We know:
\[
\frac{dl}{dt}=4\\
\frac{dw}{dt}=5
\]So:
\[
A=lw\implies\\
A'=l\frac{dw}{dt}+\frac{dl}{dt}w
\]So:
\[
A'=5l+4w
\]We evaluate this at:
\[
\frac{dA}{dt}\biggr|_{w=4, l=11}=5(11)+4(4)=71
\]
Et voilá.