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# The shaded region in the figure above represents a

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Director
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The shaded region in the figure above represents a [#permalink]  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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SVP
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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)
Current Student
Joined: 28 Dec 2004
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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!
Manager
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The length is 9*(2^(1/2)).
Manager
Joined: 28 Jan 2005
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CAn u pls include some more explanation.

Where did the 9 come from? Steps 2 and 3 are unclear[/quote]
SVP
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2wl=18*15
wl=9*15
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