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10 Jun 2022, 08:45
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The 8*18 rectangle ABCD is cut into two congruent hexagons, as shown, in such a way that the two hexagons can be repositioned without overlap to form a square. What is y?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
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66a524a2244d311dbe57cc4d9aaffc1b5e83bb03.png [ 5.88 KiB | Viewed 2333 times ]
10 Jun 2022, 10:11
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Bunuel
The 8*18 rectangle ABCD is cut into two congruent hexagons, as shown, in such a way that the two hexagons can be repositioned without overlap to form a square. What is y?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Attachment:
The attachment 66a524a2244d311dbe57cc4d9aaffc1b5e83bb03.png is no longer available
We are going to pick up the right hexagon and move it so that it sits on top of the left hexagon. The circled edge of the right hexagon will sit atop AD. AD = 8 and the circled edge is half the height, so 4. That will make the height of the square 12, so the bottom edge must also be 12. We need to cut off 6 from the 18.
Answer choice A.
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10 Jun 2022, 10:41
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The area of the rectangle is 8*18 = 144, so the square will be 12 by 12 (since the square has the same area as the rectangle), and since we need, along the bottom line, to take y away from 18 to get an edge of length 12, y must be 6.
