Related Rates - Rectangles

Question

A rectangle has a length of 2 inches and a width of 11 inches whose sides are changing. The length is decreasing by 10 in/sec and the width is growing at 8 in/sec. What is the rate of change of the area?

Answer 1

The area of the rectangle is A =xy so by the product rule dA/dt = x(dy/dt) + y(dx/dt)

If you make x the length and y the width, then x=2 in, y =11 in, dx/dt =-10 in/s (decreasing) and dy/dt= 8 in/s

so you can substitute to get the answer.