Thank you for the opportunity to help you with your question!
The dimensions that yield the greatest area is ussually square dimensions. However, since we want a rectangular enclosure, then the dimensions that yield the greatest area will be those that are close to dimensions of a square.
64 yards is the perimeter
suppose the enclosure was a square
the 32 =2l
l=32/2 = 16
however since we want a rectangular enclosure we get the values of the nearest whole number to 16. This will be 17 and 15.
Therefore 17*15 will yield the greatest area.
Please let me know if you need any clarification. I'm always happy to answer your questions.