Bunuel wrote:
A rectangular rug covers half of a rectangular floor that is 9 feet wide and 12 feet long. If the dimensions of the rug are in the same ratio as those of the floor, how many feet long
is the rug?
(A) 6
(B) 21/2
(C) 2√7
(D) 6√2
(E) 4√6
Great question. Find the ratio of width to length from floor dimensions, and then take 1/2 area of floor set equal to L*W to find rug length.
The dimensions of the rug are in the same ratio as the floor. Express W in terms of L (in order to have only variable L in the area equation). That ratio will hold for the rug.
\(\frac{W}{L}=
\frac{9}{12} = \frac{3}{4}\)
\(W = \frac{3}{4}L\)
Area of floor = 12 * 9 = 108
Area of rug is half that: 54
\(L * W\) = rug area, substitute for \(W\)
\(L *
\frac{3}{4}L = 54\)
\((\frac{3}{4})L^2 =
54\)
\(L^2 =
(54)(\frac{4}{3})\)
\(L^2 = 72\)
\(L=
\sqrt{72}=\sqrt{36*2}\)
\(L = 6\sqrt{2}\)
Answer D
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