$a+2b=100$, when $$a=2b=50$$, the largest area is $$50\times (50\div 2)=1250$$ m\textsuperscript{2}. 
Farmer Dunphy has $$100$$ metres of fencing.  He wants to make a closed rectangular pen.  He uses a long wall for one of the sides.  Each side of the pen is a whole number in metres.  What is the largest area that the pen can be? 
1: $$125\text{m}^{2}$$ 
2: $$625\text{m}^{2}$$ 
3: $$1000\text{m}^{2}$$ 
4: $$1250\text{m}^{2}$$ 
5: $$2500\text{m}^{2}$$ 