Question

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 450 m wide. How fast is the area changing at that point in time?

Answer 1

Answer:

The area is changing at the point of  $\mathbf{61200 m^2/year}$

Step-by-step explanation:

From the given information:

Let's recall from our previous knowledge that the formula for finding the area of a rectangle = L × w

where;

L = length and w = width of the rectangle

Suppose the Length L is twice the width w

Then L = 2w --- (1)

From The area of a rectangle

A = L  × w

A = 2w  × w

A = 2w²

Taking the above differentiating with respect to time

$\dfrac{dA}{dt }= 4w \times \dfrac{dw}{dt} --- (2)$

At the time t

$\dfrac{dw}{dt}= 34 m \ per \ year ; w = 450 \ m$

Replacing the values back into equation 2, we get:

$\dfrac{dA}{dt }= 4 \times 450 \times 34$

$\mathbf{\dfrac{dA}{dt }= 61200 m^2/year}$