Step-by-step explanation:
Let x be the width of the uniform strip floor around the rug.
Then the width of the rug is (21 - 2x) and the length of the rug is (29 - 2x).
(21 - 2x)(29 - 2x) = 345
609 - 100x + 4x^2 = 345
4x^2 - 100x + 264 = 0
x^2 - 25x + 66 = 0
(x - 22)(x - 3) = 0
x = 3 or x = 22 (rejected as x must be less that the width of the room)
Hence the width of the rug is 21 - 2(3) = 15 feet and the length of the rug is 29 - 2(3) = 23 feet.
