Find the largest possible rectangular area you can enclose with 420 meters of fencing. What is the significance of the dimensions of this enclosure, in relation to geometric shapes?

I believe the ultimate fenced in area with minimal perimeter is a square.

For any geometric shape a circle has the greatest maximum area minimum perimeter ratio.

So for 420 meters, a square with sides of 105 meters will enclose maximum area if you must fence in a rectangular shape.