Can someone please help me with this Geometry problem? I would really appreciate the help!

Question

Brett is buying a rug for his living room. His living room is a rectangle with a length that is twice as long as its width. Brett decides that the rug will also be a rectangle, but it will be only one half the length of the room and one half as wide. What will be the ratio of the rug’s area to the living room’s area?

Answer 1

Regardless of the room's dimensions, the rug's area will be 1/4 the area of the room. Here's a quick way to show this:

Suppose the room is w feet wide and l feet long. The area of the room is w*l. The rug will be (w/2) feet wide and (l/2) feet long. So the area of the rug is (w/2)*(l/2), which equals (w*l)/4, or one quarter the area of the room.

Note that the living room being twice as long as it is wide is extraneous information.