Question

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!)

Answer 1

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!