The reducing factor is 1/5. The rectangular rug 12.5 feet long and 10 feet wide needs to be reduced by a factor of 1/5.
The area of the reduced rug will be the new long times the new wide.
New long = 12.5 feet * 1/5 = 2.5 feet
New wide = 10 feet * 1/5 = 2.0 feet
New area = 2.5 feet * 2.0 feet = 5.0 feet^2.
Answer: 5.0 ft^2