Jun has 240 meters of fencing to make a rectangular enclosur

Jun has 240 meters of fencing to make a rectangular enclosure. She also wants to use some fencing to split the enclosure into two parts with a fence parallel to two of the sides. What dimensions should the enclosure have to have the maximum possible area? (Enter your answers as a comma-separated list.)

Solution

let us assume
x = length of three parallel sections
(240 - 3x) / 2 = length of the two remaining sides
A = total area of enclosure
so
A(x) = x(240 - 3x)/2
        = 120x - 3/2x²
and so, A is maximized wne A\' = 0
so
A\'(x) = 120 - 3x we have applied the power rule
and
0 = 120 - 3x
3x=120
hence,
x = 40
now,
x = length of three parallel sections=40m
(240 - 3x) / 2 = length of the two remaining sides =(240-3*40)/2=120/2=60m