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19 Feb 2025, 22:53
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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Question Stats:
100% (00:47) correct
0% (00:00) wrong based on 1 sessions
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In the figure below, diagonal EG of square EFGH is 1/2 of diagonal AC of the square ABCD. What is the ratio of the area of the shaded region to the area of ABCD?
A. \(\sqrt{2}:1\)
B. 3:4
C. \(\sqrt{2}:2\)
D. 1:2
E. \(1:2:\sqrt{2}\)
12.jpg [ 13.04 KiB | Viewed 177 times ]
A. \(\sqrt{2}:1\)
B. 3:4
C. \(\sqrt{2}:2\)
D. 1:2
E. \(1:2:\sqrt{2}\)
Attachment:
12.jpg [ 13.04 KiB | Viewed 177 times ]
22 Feb 2025, 10:36
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OE
Obviously, the shaded region is smaller than square ABCD, so the ratio must be less than 1. Eliminate A. Also, from the diagram, it is clear that the shaded region is more than half of square ABCD, so the ratio is greater than 0.5. Eliminate D and E. Since 3:4 = .75 and \(\sqrt{2}:2 ≈ .71\), B and C are too close to tell which is correct just by looking; so guess.
The answer is B.
Obviously, the shaded region is smaller than square ABCD, so the ratio must be less than 1. Eliminate A. Also, from the diagram, it is clear that the shaded region is more than half of square ABCD, so the ratio is greater than 0.5. Eliminate D and E. Since 3:4 = .75 and \(\sqrt{2}:2 ≈ .71\), B and C are too close to tell which is correct just by looking; so guess.
The answer is B.
