The room is 10 feet long by 9 feet wide. If a 5 ft by 7 ft rug is placed in the room how much of the floor will not be covered?

The area of the room is 10 feet x 9 feet = 90 square feet.

The area of the rug is 5 feet x 7 feet = 35 square feet.
Therefore, the area of the floor that will not be covered by the rug is:

90 square feet - 35 square feet = 55 square feet.

So, 55 square feet of the floor will not be covered by the rug.