Question

The length of a rectangle is increasing at a rate of 1 meter per day and the width is decreasing at a rate of 2 meters per day. When the length is 8 meters and the width is 18 meters, then how fast is the AREA changing?

Answer 1

The area is changing at 2 m²/d.

Explanation:

The area of a rectangle is given by:

`A = l*w`

Where:

l is the length

w is the width

We have that the length is increasing at a rate:

`(dl)/(dt) = 1 (m)/(d)`

And the width is decreasing at a rate:

`(dw)/(dt) = -2 (m)/(d)`

The change in the rectangle's area is the following:

`(dA)/(dt) = w(dl)/(dt) + l(dw)/(dt)`

When the length is 8 meters and the width is 18 meters we have:

`(dA)/(dt) = 18 m*1(m)/(d) + 8 m(-2 (m)/(d))`

`(dA)/(dt) = 18 (m^(2))/(d) - 16 (m^(2))/(d)`

`(dA)/(dt) = 2 (m^(2))/(d)`

Therefore, the area is changing at 2 m² per day.

I hope it helps you!