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Answer:
100m by 50m.
Step-by-step explanation:
Let the dimension of the rectangular pen be x and y
Area, A(x,y)=xy
Let the side opposite her barn = x
Since she wants to fence only three side
Perimeter = x+2y
Length of Fencing Available = 200m
Therefore:
We want to maximize the area of the pen, A(x,y).
Substituting x=200-2y into A(x,y)=xy
To maximize A(y), we find its derivative and solve for the critical points.
To ensure that this is a maximum, we use the second derivative test.
This is negative and thus, y=50 is a maximum point.
Recall:
x=200-2y
x=200-2(50)
x=200-100
x=100m
Therefore, the dimensions of the pen that has the largest area are 100m by 50m.