How the area of the original rectangle change when the length and width are both doubled?

When both the length and width of an original rectangle are doubled, the area increases by a factor of four. This is because the area of a rectangle is calculated by multiplying its length by its width. If the original dimensions are ( l ) (length) and ( w ) (width), then the new area becomes ( (2l) \times (2w) = 4lw ), which is four times the original area.