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:

answer 1 : option "c"

answer 2 : option "d"

answer 3 : option "b"

answer 4 : option "d"

answer 5 : option "b"

answer 6 : option "a"

answer 7 : option "c"

answer 8 : option "d"

answer 9 : option "c"

answer 10 : option "d"

answer 11 : option "c"

answer 12 option "b"

answer 13 option "c"

answer 14 option "c"

answer 15 option "d"

answer 16 option "a"

answer 17 option "b"

answer 18 option "c"

answer 19 option "a"

answer 20 option "a"

answer 21 option "c"

d

one set of data has more variation than the other. hope this !