can you just show me how to set this up? or a formula that could help? im confused.

Question

The length of a rectangle is increasing at 3 ft/min and the width is decreasing at 2 ft/min. When the length is 50 ft and the width is 20 ft, at what rate is the rectangle decreasing?

Answer 1

Let the width of the rectangle be x ft
let the length of the rectangle be y ft

Area = xy
d(Area)/dt = x dy/dt + y dx/dt

given: dx/dt = -2 and dy/dt = 3
so when x = 20 and y = 50

d(Area)/dt = 20(3) + 50(-2)
= -40

At that moment, the area is decreasing at a rate of 40 ft^2/min

Answer 2

thank you so much!!!!