Ms. Osborne asks each student in her class to draw a rectangle with integral side lengths and a perimeter of $$50$$ units. All of her students calculate the area of the rectangle they draw. What is the difference between the largest and smallest possible areas of the rectangles? 
Overseas Competition->Knowledge Point->Geometry Modules->Objects with Straight Sides->Knowing Graphs
As we know, the sum of the length and width is $$25$$. The largest area is $$13\times12=156$$ and the smallest area is $$24\times1=24$$, so the difference is $$156-24=132$$. 