posted by anonymous .
How should this be done?
Suppose you have 132 m of fencing with which to make two side-by-side rectangular enclosures against an existing wall. if the rectangular enclosures are adjacent and of the same depth what is the maximum are that can be enclosed?
Let the combined length of the two rectangles by y
let the width be x (there will be 3 of those)
so 3x + y = 132
y = 132-3x
Area = xy
= -x^2 + 132x
d(Area)/dx = -2x + 132 = 0 for a max of Area
x = 66
then max Area = 66(132-66) = 4356 m^2
by completing the square:
Area = -[x^2 - 132x + 4356 - 4356 ]
= -(x-66)^2 + 4356
so the max Area is 4356 , when x = 66