The dimensions are 25 * 50 feet.
The 3 sides of the pen will measure (2x + y) feet where x is the width and y is the length.
2x + y = 100
y = 100 - 2x
The area A = xy = x(100 - 2x) ft^2.
Finding the maximum area.
A = x(100 - 2x)
A = 100x - 2x^2 Finding the derivative:
A' = 100 - 4x
For maximum value of A this equals zero:
100 - 4x = 0
4x = 100
x = 25 ft, so this is the width.
The length is 100 - 2(25) = 50 ft.