Rate/Relations Calc I Area of Rectangle

[QuarkCharmer]

Homework Statement

Stewart Calculus 6E, 3.8 #4
4.) The length of a rectangle is increasing at a rate of 8cm/s and its width is increasing at a rate of 3cm/s. When the length is 20cm and the width is 10cm, how fast is the area of the rectangle increasing?

Homework Equations

A = LW

The Attempt at a Solution

I am not entirely sure how to set this problem up. I think I would start with A=LW, and then implicitly differentiate to:

[tex]A' = L'W + W'L[/tex]

Then perhaps, plug in my values for the change in length and width as so:
[tex]A' = 8W + 3L[/tex]

But that doesn't seem right?

 

[rock.freak667]

I think that is correct.

 

[QuarkCharmer]

So, in that equation the W and L non prime can be put, so that:
[tex]A' = 8(10)+3(20)[/tex]

So the rate of the area when the sides are width:10 length 20 is 140cm^2/s ??

 

[rock.freak667]

That should be correct or how I would do the question.