Question 340367
Assume a rectanglular shape

We know that the largest rectabgle area for a given perimeter is a square.

{{{Area = x * y}}} 
{{{AreaSquare = x^2}}}
Add in 100 more feet of perimeter. 
100/4 means each side of the square is now 25 feet longer than before.
{{{NewAreaSquare = (x+25)^2}}}
{{{NewArea = x^2 + 50x + 625}}}
Difference is then {{{50x+625}}}