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So the pen will have only 3 sides of fencing.
Let each of the 2 short sides be x
let the long side by y
2x + y = 150
y = 150 - 2x
Area = A = xy
A = x(150 - 2x) = -2x^2 + 150x
This is a downwards opening parabola, and the vertex will tell us
what the maximum area is , and for what x it will happen.
You must be studying how to find that vertex, the simplest is this:
the x of the vertex is -150/-4 = 75/2
then y = 150 - 2(75/2) = 75
max area = xy = (75/2)(75) = 5625/2 ft^2