Answer:
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: