SOLUTION: A decorator plans to place a rug in a room with the dimensions of 9 meters by 12 meters in such a way that a uniform strip of flooring around the rug will remain uncovered. If the

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Question 252087: A decorator plans to place a rug in a room with the dimensions of 9 meters by 12 meters in such a way that a uniform strip of flooring around the rug will remain uncovered. If the rug is to cover 1/2 the floor space, what should the dimensions of the rug be?
equation and answer please.
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
9*12=108 sq meters
so only 54 sq meters are to be covered
9*6 is neat and clean but the decorator wants the rug to be centralized in the room with even space around it. This would leave exactly one half of the room bare
(9-x)(12-x)=54
108-21x+x^2=54
54-21x+x^2
x=3 and x=18
x=18 gives us negative dimensions
6*9 actually gives us 1.5 meters all around.
but the rug will be turned so that the length of 9 meters will go on the 12 meter length of the room.