The back of jill's property is a creek. jill would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a corral. if there is 500 feet of fencing available, what is the maximum possible area of the corral?

Step-by-step explanation:

Let's define some notation first :

w= width , l = length , A= Area, P perimeter

For this case we want to maximize the Area given by this function:

A= l w   (1)

With the following restriction P=500 ft

We know that the perimeter on this case is given by:

Since they are using the creek as one side.

So then we have this:

  (2)

Now we can solve w in terms of l from eqaution (2) and we got:

  (3)

And we can replace this condition into equation (1) like this:

And we can maximize this function derivating respect to l and we got:

And then we got that

And if we solve for w from equation (3) we got:

And then the dimensions would be:

And the area would be:

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step-by-step explanation:

step-by-step explanation: