Question

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?

Answer 1

Lets apply sone logic here. We know for a fact that 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.

The significance of the dimensions will be that all sides of the rectangle will be equal, I.e. it will be a square

The largest area is the record 105*105cm^2 = 11025 m^2