You want to build a 3 sided fence on the back of a building using 100 feet of fencing. What dimensions of the

Question

What dimensions of the pen will yield the greatest area?

Answer 1

if width = w, then length = 100 - 2w, and for maximum area take derivative of area's function: w(100 - 2w); f'(w) = 100 - 4w, and setting this to 0, we get 4w = 100, so w = 25, and length = 50

Answer 2

2y+x=100 x(y) = area

x = 100 - 2y

(y) ( 100 - 2y ) = area
100y - 2y^2 = area
100 - 4y = 0
y = 25

So the three side are 25, 50 and 25 for a maximu area of 1250 square feet

Answer 3

50 ft x 25 ft = 1250 ft^2