Question

a rectangular pen is to be constructed alongside a barn using 120 feet of fencing. the barn will be used for one side of the pen. What should the dimensions of the pen be to maximize its area.

***Can not use calculus. This is a 9th grade question

Answer 1

If the sides have length a and b, then, assuming b is the side parallel to the barn,

a+a+b = 120, so b = 120-2a
Area = a*b = a*(120-2a) = 120a - 2a² = 2a(60-a)

Now, this is a parabola opening downward. The vertex (a maximum) is halfway between the roots, 0 and 60, at a=30

So, pen is 30x60 feet.