Question

Farmer Ed has
9,000 meters of​ fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the​ river, what is the largest area that can be​ enclosed?

Answer 1

x = length
y = width

x + 2 y = 9000 or x = 9000 - 2 y
A = x y
so
A = (9000-2y)y

2 y^2 - 9000 y = - A
y^2 - 4500 y = -A/2

y^2 - 4500 y +(4500/2)^2 = -A/2 + 5,062,500

(y-2250)^2 = -(1/2)(A-10,125,000)
so
width = 2250
length = 4500
area = 10,125,000 m^2