Question 992571
The border will be inside the dimensions of the room, therefore
(19-2x) * (18-2x) = 272
342 - 74x + 4x^2 = 272
rearrange the terms
4x^2 - 74x + 342 = 272
divide both sides of = by 4
x^2 - 18.5x + 85.5 = 68 
subtract 68 from both sides of =
x^2 - 18.5x + 17.5 = 0
use quadratic formula to solve for x
x = (-(-18.5) + sqrt((18.5^2)−(4×17.5))) / 2 = 17.5
x = (-(-18.5) - sqrt((18.5^2)−(4×17.5))) / 2 = 1
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The reasonable dimension for the strip around the rug is 1 foot, therefore
the dimensions for the rug are 17 feet long and 16 feet wide