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In the figure above, if two identical rectangles overlap to form three

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In the figure above, if two identical rectangles overlap to form three [#permalink]

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New post 11 Oct 2017, 00:49
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In the figure above, if two identical rectangles overlap to form three regions with areas 12, 6, and R, respectively, then R =

(A) 6
(B) 12
(C) 15
(D) 18
(E) 24

[Reveal] Spoiler:
Attachment:
2017-10-11_1127_001.png
2017-10-11_1127_001.png [ 3.86 KiB | Viewed 518 times ]
[Reveal] Spoiler: OA

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Re: In the figure above, if two identical rectangles overlap to form three [#permalink]

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New post 11 Oct 2017, 01:18
Assuming that y is the total length of rectangle and not of each smaller rectangle.
xy=12+6=18
Also, xy=R+6
Therefore, R+6=18
R=12
Answer B.
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Re: In the figure above, if two identical rectangles overlap to form three [#permalink]

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New post 11 Oct 2017, 08:01
This seems too easy...am I missing something here? :| :think:

Since the rectangles are identical, and assuming the region with area 6 does not overlap region with areas 12 or R:
Area of both rectangles will be equal
R + 6 = 12 + 6
R = 12

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Re: In the figure above, if two identical rectangles overlap to form three [#permalink]

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New post 11 Oct 2017, 08:38
My understanding R=12, Can some one confirm?
Or am I missing anything!!

Thanks.

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Re: In the figure above, if two identical rectangles overlap to form three [#permalink]

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New post 11 Oct 2017, 10:25
The area of a single of the overlapping rectangles can be expressed as x*y

From the figure we can formulate that:

(1) x*y = 12+6 = 18

(2) x*y = R+6

From (1) and (2): 12+6 = R+6 => R = 12

Answer: B

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In the figure above, if two identical rectangles overlap to form three [#permalink]

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New post 13 Oct 2017, 09:29
Bunuel wrote:
Image
In the figure above, if two identical rectangles overlap to form three regions with areas 12, 6, and R, respectively, then R =

(A) 6
(B) 12
(C) 15
(D) 18
(E) 24

[Reveal] Spoiler:
Attachment:
2017-10-11_1127_001.png


Since the two rectangles are identical, their areas are equal also. Since they overlap a region with area 6, their non-overlap regions should have equal areas also. Since one of the rectangles has a non-overlap region of area 12, the other rectangle also has a non-overlap region of area 12. That is, R = 12.

Answer: B
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Kudos [?]: 906 [0], given: 5

In the figure above, if two identical rectangles overlap to form three   [#permalink] 13 Oct 2017, 09:29
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