An inner city revitalization zone is a rectangle that is twice as long as it is wide. The width of the region is growing at a rate of 34 m per year at a time when the region is 260 m wide. How fast is the area changing at that point in time

Using implicit differentiation, it is found that the area is changing at a rate of 35360 m²/year.

The area of a rectangle of length l and width w is given by:

Applying implicit differentiation, we the rate of change is given by:

In this problem:

Also:

Since

Then:

The area is changing at a rate of 35360 m²/year.

A similar problem is given at link

The rate of change of area is 35360 m /year

Step-by-step explanation:

Let the width of rectangle be w

We are given that  a rectangle that is twice as long as it is wide

So, Length of Rectangle  = 2w

Area of rectangle A = Length \times Breadth =

Differentiating area with respect to time

We are given that and w = 260

Hence the rate of change of area is 35360