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# In the figure above, two rectangular regions overlap. If the area of

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Math Expert
Joined: 02 Sep 2009
Posts: 44398
In the figure above, two rectangular regions overlap. If the area of [#permalink]

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12 Nov 2017, 10:19
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In the figure above, two rectangular regions overlap. If the area of region ABCD is 20, what is the perimeter of the shaded region?

(A) 22 – √17
(B) 31 – 2√5
(C) 31 – √17
(D) 28
(E) 31

[Reveal] Spoiler:
Attachment:

2017-11-12_2102_001.png [ 10.5 KiB | Viewed 358 times ]
[Reveal] Spoiler: OA

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In the figure above, two rectangular regions overlap. If the area of [#permalink]

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12 Nov 2017, 13:02
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2017-11-12_2102_001.png [ 13.17 KiB | Viewed 279 times ]

The second rectangle which overlaps the rectangle ABCD is PQST

The triangle EFG so formed is right angled at F,
which will have a hypotenuse = $$\sqrt{1+4^2}$$ or $$\sqrt{17}$$

Perimeter of the shaded region = PQ+QS+ST+GD+CD+CE+PT-hypotenuse =$$4+7+4+3+2+4+7-\sqrt{17}$$

Therefore, the perimeter of the shaded portion is $$31-\sqrt{17}$$(Option C)
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In the figure above, two rectangular regions overlap. If the area of   [#permalink] 12 Nov 2017, 13:02
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