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The figure below shows the dimensions of a square picture

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The figure below shows the dimensions of a square picture [#permalink] New post 02 Jan 2007, 17:12
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The figure below shows the dimensions of a square picture frame that was constructed using four pieces of frame as shown. If w is the width of each piece of the frame, what is the area of each piece?

(1) w = 3 inches
(2) PQ = sq root (18) inches
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2007-01-02_114321_z.jpg
2007-01-02_114321_z.jpg [ 3.01 KiB | Viewed 185 times ]

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 [#permalink] New post 02 Jan 2007, 17:39
(1) suff

Area of outer square = 3 ft ^2
Area of inner square = (36inch - 6inch) ^ 2
Area of each piece = difference between the area of the squares/4

(2) suff

Diagonal of outer square = 3 * sqrt (2)
Diagonal of innter square = 3 * sqrt (2) - 2 * PQ
side of inner square can be found
and area can be determined

Last edited by dred on 02 Jan 2007, 18:04, edited 1 time in total.
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 [#permalink] New post 02 Jan 2007, 17:50
D

From (i) PQ represents the diagonal of a small square between the 2 edges of the large and the small square.

PQ should be sqrt(2)*3

ii) From the size of PQ also we can find out the relative size of the smaller square
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 [#permalink] New post 03 Jan 2007, 14:15
Assuming each piece of the frame has the same dimensions as the others, we can know the area of each piece knowing either its width or the length of the diagonal sides. Therefore, D.
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 [#permalink] New post 04 Jan 2007, 14:26
Thanks Guys...OA is D
  [#permalink] 04 Jan 2007, 14:26
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