I've asked the same question two other times, and i used almost 100 points between the two. if you want you can even answer it on the last question where i used 75 points.

a farmer wants to build a rectangular pen. he plans to use a wall of his barn for one side of the pen. he has 76 yards of fencing material.

what is the maximum area that can be enclosed?

To max the area, make sure te length=width
so

76 yards of fencing, that is perimiter
so
P=2(L+W)
76=2(L+W)
if L=W then
76=2(L+L)
76=2(2L)
76=4L
divide both sides by 4
19=L=W

the area is length times width=19*19=361 square feet
remember that the definition of a rectangle is 4 right angles, it is not required to have different length sides. all squares are rectangles but not all rectanlges are squres, just sayin for that one person who always tells me that I'm wrong because it's a square

max area is 361 square feet

20000 as first it increases by 2500 then by 5000 so next it will increase by 10000