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ABCD is a square picture frame (see figure). EFGH is a square centered

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ABCD is a square picture frame (see figure). EFGH is a square centered [#permalink] New post   06 Feb 2023, 02:04
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ABCD is a square picture frame (see figure). EFGH is a square centered within ABCD as a space for a picture. The area of EFGH (for the picture) is equal to the area of the picture frame (the area of ABCD minus the area of EFGH). If AB = 6, what is the length of EF?

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\(3 \sqrt{2}\)
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Re: ABCD is a square picture frame (see figure). EFGH is a square centered [#permalink] New post   20 Feb 2023, 07:55
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The area of the frame and the area of the picture sum to the total area of the image, which is 62, or 36. Therefore, the area of the frame and the picture are each equal to half of 36, or 18. Because EFGH is a square, the length of EF is

\(\sqrt{18}=3 \sqrt{2}\)
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Re: ABCD is a square picture frame (see figure). EFGH is a square centered [#permalink]
20 Feb 2023, 07:55
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