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

Answer:

The area is changing at 2 m²/d.

Step-by-step 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:

$\frac{dl}{dt} = 1 \frac{m}{d}$

And the width is decreasing at a rate:

$\frac{dw}{dt} = -2 \frac{m}{d}$

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

$\frac{dA}{dt} = w\frac{dl}{dt} + l\frac{dw}{dt}$

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

$\frac{dA}{dt} = 18 m*1\frac{m}{d} + 8 m(-2 \frac{m}{d})$

$\frac{dA}{dt} = 18 \frac{m^{2}}{d} - 16 \frac{m^{2}}{d}$

$\frac{dA}{dt} = 2 \frac{m^{2}}{d}$

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

I hope it helps you!