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The shaded region in the figure above represents a

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The shaded region in the figure above represents a [#permalink] New post 27 Jan 2005, 19:55
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The shaded region in the figure above represents a rectangular frame with length 18 inches and width 15 inches. The frame encloses a rectangular picture that has the same area as the frame itself. If the length and width of the picture have the same ratio as the length and width of the frame, what is the length of the picture, in inches?
(A) 9 * (2^1/2)
(B) 3/2
(C)9 / (2^1/2)
(D) 15[1- 1/(2^1/2)]
(E) 9/2
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 [#permalink] New post 27 Jan 2005, 20:19
l/w=18/15=6/5 => w=5/6*l
wl=18*15-wl =>wl=9*15

5/6l^2=9*15
l^2=9*18
l=9*2^(1/2)
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 [#permalink] New post 28 Jan 2005, 07:32
I had a strange way of doing it...I guess I get lucky since I get a fairly close estimate....

l/w=18/15=6/5
area 18*15=270

frame must have area half of this....270/2=135!

w=5/6l, area must 5/6l*l=135
l^2=810/5=165, sqrt of (165)~ 9sqrt(2)!

what do you guys make of my approach!
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 [#permalink] New post 28 Jan 2005, 12:54
The length is 9*(2^(1/2)).
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 [#permalink] New post 31 Jan 2005, 03:37
CAn u pls include some more explanation.

Where did the 9 come from? Steps 2 and 3 are unclear[/quote]
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 [#permalink] New post 31 Jan 2005, 07:14
2wl=18*15
wl=9*15
  [#permalink] 31 Jan 2005, 07:14
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