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Rectangular frame

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Rectangular frame [#permalink] New post 18 Mar 2010, 13:34
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Can some one help me with this question? Answer is A

A rectangular frame with length 18 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)9/12
D15(1-1/(2)^1/2
E)9/2


The was I was approaching this question was that I found the ratio of 18:15, that is 6:5
and then trying to find the length with the given answer options to see if i can get the same area as 18*15=270.

I get [9(2)^1/2 *5/6] *9(2)^1/2 which is equal to 135. I dont see how this will be equal to 270. Maybe I dont understand the question properly.
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Re: Rectangular frame [#permalink] New post 18 Mar 2010, 14:02
Let x and y are length and breath of frame.
Let a and b are length and breadth of picture

given frame area = area of picture that means 2ab=xy ---------------(1)

also a/b = x/y = 6/5 => b = 5a/6

Now put b = 5a/6 and xy = 18*15 in equation (1), you will get a = 9(2)^1/2
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Re: Rectangular frame [#permalink] New post 18 Mar 2010, 14:11
Thank you!! can you suggest any more questions to practice off?
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Re: Rectangular frame [#permalink] New post 19 Mar 2010, 04:38
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Re: Rectangular frame [#permalink] New post 20 Mar 2010, 18:58
How can you say 2ab=xy when the area is the same?
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Re: Rectangular frame [#permalink] New post 21 Mar 2010, 05:36
cshenba wrote:
How can you say 2ab=xy when the area is the same?


Let x and y are length and breath of frame.
Let a and b are length and breadth of picture

now total area = area of picture + area enclosed between frame and picture.

its given area of picture = area enclosed between frame and picture.

=> xy = ab + ab => xy = 2ab
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Re: Rectangular frame   [#permalink] 21 Mar 2010, 05:36
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