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Answer:
5.055 m by 13.055 m
Step-by-step explanation:
Let x represent the width of the room in meters. Then the length is x+8 meters, and the room area is ...
A = LW = (x+8)(x) = 2(rug area)
x^2 +8x = 2(3)(11) = 66
Completing the square, we have ...
x^2 +8x +16 = 82
(x +4)^2 = 82
x = -4 ±√82 ≈ {-13.055, +5.055}
The magnitudes of these dimensions are the dimensions of the room:
√82 ± 4 = {5.055, 13.055} . . . meters
Therefore, the room is 5.055 × 13.055 meters.
