Area that can be enclosed

Question

farmer ed has 8,000 meters of fencing and wants to enclose a rectangular plot that borders the river. If Farmer Ed does not fence along side of the river, what is the largest area that can be enclosed? length is 8,000-2x and width is x

Answer 1

max area = 4000 times 2000 = 8,000,000 = 8 million square meters

area = A = Lw = (8000-2x)(x) = 8000x -2x^2

max A is when A' = 0 = 8000 -4x

x = 8000/4 = 2000 meters

and 8000-2x = 4000 meters

max A = Lw = 4000(2000) = 8,000,000 m^2