The smiths want to buy a 9 ft. by 12 ft. carpet and center it in a 15 ft. by 20 ft. room. can a 3 1/2 foot by 12 foot couch be placed against one of the long walls of the room without touching the carpet? can a 3 1/2 foot by 12 foot couch be placed against one of the short walls of the room without touching the carpet?

To answer this question, you should draw a picture of a large rectangle with labels 15 ft by 20 ft.

Inside the large rectangle, draw another rectangle (the carpet) with dimensions 9 ft by 12 ft.

When you do this, you will see that you will have 3 feet of space on both sides of the longer wall (15 - 9 = 6; 6/2 = 3 feet).

On the shorter wall, you will have 4 feet of space (20 - 12 = 8; 8/2 = 4 feet).

You will have room for your couch on the shorter wall without touching the carpet.