Hyp + B =400
Hyp = 400 - B.
Let the length of the barn side of the enclosure be x, thenb) Fidn the function A(B), the area of the pen as a function of the length of it's base. You do not need to simplify your answer.
A(B) = B*x/2,
Hyp^2 = x^2 + B^2
or substituting Hyp from part a):
(400-B)^2 = x^2 + B^2
x^2 = (400-B)^2 - B^2 = 160000 -800 B
Plug into the area formula:
A(B) = (1/2) B sqrt(160000 - 800 B)