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?

Yes duh

No.

Can a 3 1/2 foot by 12 foot couch be place against one of the short walks of the riim 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 determine if the couch can be placed against one of the long walls without touching the carpet, we need to calculate the space left on that wall after the carpet is centered in the room.

First, let's find out the dimensions of the room remaining on the selected wall after the carpet is placed.

The room dimensions are given as 15 ft. by 20 ft., and we need to center a 9 ft. by 12 ft. carpet. This means there will be a remaining space around the carpet of (15 ft - 9 ft)/2 = 6 ft on the shorter wall and (20 ft - 12 ft)/2 = 4 ft on the longer wall.

To determine if the couch can fit without touching the carpet, we need to calculate the combined width of the couch and the space it will occupy on the wall.

The couch is given as 3 1/2 ft. wide and we want to place it against the longer wall. So, we add the width of the couch (3 1/2 ft.) to the space available (4 ft.) on the wall, giving us a total of 3 1/2 ft + 4 ft = 7 1/2 ft.

Since the combined width of the couch and the space it will occupy (7 1/2 ft.) is less than the remaining space on the longer wall (4 ft.), we can conclude that the couch can be placed against one of the long walls without touching the carpet.