## anonymous 3 years ago 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?

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.