A pet boarding facility wants to build two adjacent pens of equal size. They are using the length of the dog kennel as one side of the two pens. They have 324 feet of fencing to build the pens. What width should he make the pens to maximize the total area of the pens?

Answer 1

fence=3w+l=324

area=lw=(324-3w)w
zeroes at w=0, w=325/3

so max should be 1/2 way between the two zeroes, or max w=324/6=54
l=324-3(54)=you do it.

Answer 2

A square pens will give you the maximum area. To build 2 adjacent square pens with one common side, you will need 6 equal lenghts of fence.
324/6 = 54
Area of each square pens = 54×54=2916 sq ft

Answer 3

I forgot to mention that the lenght of the dog kennel is the common side and therefore need not taken from the available fencing.