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

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Math Expert
Joined: 02 Sep 2009
Posts: 50619
In the figure above, if two identical rectangles overlap to form three  [#permalink]

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10 Oct 2017, 23:49
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Difficulty:

5% (low)

Question Stats:

98% (01:15) correct 2% (00:42) wrong based on 59 sessions

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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

Attachment:

2017-10-11_1127_001.png [ 3.86 KiB | Viewed 958 times ]

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

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11 Oct 2017, 00:18
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
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Re: In the figure above, if two identical rectangles overlap to form three  [#permalink]

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11 Oct 2017, 07:01
This seems too easy...am I missing something here?

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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11 Oct 2017, 07:38
My understanding R=12, Can some one confirm?
Or am I missing anything!!

Thanks.
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Joined: 06 Oct 2017
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Re: In the figure above, if two identical rectangles overlap to form three  [#permalink]

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11 Oct 2017, 09:25
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

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

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13 Oct 2017, 08:29
Bunuel wrote:

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

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.

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In the figure above, if two identical rectangles overlap to form three &nbs [#permalink] 13 Oct 2017, 08:29
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