Let the pen have sides length a and b (both in ft)
If we assume that the sides for the separate internal pens are parallel to the sides of the outer pen then
3a+3b=1200 ft or a+b=400 ft
and the area=ab or a=area/b
substitute in the equation above
area/b + b = 400 ft
area = 400b-b^2
which is a maximum when
400 ft = 2b or b=200 ft, hence a=200 ft
But check the maths!
1. Farmer Brown has 1200ft of fence to create a rectangular pen.
If he would like to separate the pen into 4 areas, what dimensions will maximize and what is the maximum area? (Do not forget units!)
1 answer