The length of a rectangle is decreasing at a rate of 2 meters per minute and the width is increasing at a rate of 5 meters per minute.

Question

When the length is 10 meters and the width is 24 meters, then how fast is the AREA changing?

The rate of change of AREA is _____ square meters per minute.

(Enter your answer as an integer.)

Answer 1

The length decreasing 2 meters per minute means:

dl/dt = -2

The width increasing 5 meters per minute means:

dw/dt = 5

The formula for the area of a rectangle is:

A = w * l

Use implicit differentiation and the product rule to find dA/dt:

dA/dt = w * dl/dt + dw/dt * l

Plug in the values that we have for length, width, change in length, and change in width:

dA/dt = 24 * (-2) + 5 * 10

dA/dt = 2

So the rate of change of the area is 2 square meters per minute.