Question

A farmer is making a pig pen next to the barn. He has enough materials to build 50 feet of fencing.

a)what is the largest area he can fence in?

b)what are the dimensions of the pen with the largest area?

Answer 1

One side of the barn counts as an enclosure.

Answer 2

length = 50-2w

area = w(50-2w)
max area at w=25/2

Answer 3

One side of the barn counts as one side of the fence. You are left with one L (length) and 2W (width). Set L=y and W=x. xy=Area(A) and 2x+y=Total Fence(50ft). Subtract 2x over to get y=50-2x. Substitute for y into the area formula to get A=x(50-2x) = A=-2x^2+50x. Use the formula x=-b/2a where a=-2 and b=50, so x=-50/(2*-2) so x=12.5ft, and y=25ft.
a) The largest area is 12.5*25=312.5ft
b)The dimensions are 12.5 by 25 ft