Question 759141
Say you're given 100 ft of fencing. You want to maximize what you can get out of all that fencing (with minimal waste and redundancy). This means you want to maximize the area that the fence can enclose. 


The reason the perimeter is fixed is because you often know how much fencing you have (you can measure it if you don't know) or you can specify how much you are willing to buy (mainly based off a set fixed budget). So knowing how to maximize the area will minimize the cost in a way because you are effectively getting the most out of your money. You also save time because you don't have to construct areas by trial and error if you know the exact shape you want to build before you actually do it.