How does doubling the side length of a rectangle affect its area

Doubling the side-lengths will multiply the area by four.

Proof:
Let the side-lengths of the rectangle by x and y.  Clearly, the area will be x*y=xy.  The new rectangle will have side-lengths 2x and 2y, and thus area 2x*2y=4xy.  4xy/xy=4 - hence, the new rectangle has four times the area of the old one.