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# In the rectangle above, the shaded square regions A and B are to be

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Joined: 02 Sep 2009
Posts: 47037
In the rectangle above, the shaded square regions A and B are to be [#permalink]

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26 Sep 2017, 23:22
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Question Stats:

56% (01:36) correct 44% (01:14) wrong based on 25 sessions

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In the rectangle above, the shaded square regions A and B are to be folded along lines PQ and RS respectively onto rectangular region X. What will be the area, in square inches, of the part of A that overlaps with B?

(A) 5
(B) 10
(C) 15
(D) 20
(E) 25

Attachment:

2017-09-27_1015_001.png [ 5.88 KiB | Viewed 662 times ]

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Re: In the rectangle above, the shaded square regions A and B are to be [#permalink]

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27 Sep 2017, 07:53
Bunuel wrote:

In the rectangle above, the shaded square regions A and B are to be folded along lines PQ and RS respectively onto rectangular region X. What will be the area, in square inches, of the part of A that overlaps with B?

(A) 5
(B) 10
(C) 15
(D) 20
(E) 25

Attachment:
2017-09-27_1015_001.png

when the Square A overlaps rectangle PR then the length of the region not overlapped is 2.
Similarly the length of the region not overlapped by B is 2 so the area overlapped will have length 3 so the area would be 3*5=15
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In the rectangle above, the shaded square regions A and B are to be [#permalink]

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27 Sep 2017, 12:00
Bunuel wrote:

In the rectangle above, the shaded square regions A and B are to be folded along lines PQ and RS respectively onto rectangular region X. What will be the area, in square inches, of the part of A that overlaps with B?

(A) 5
(B) 10
(C) 15
(D) 20
(E) 25

Attachment:
The attachment 2017-09-27_1015_001.png is no longer available

Attachment:

trifold.png [ 9.28 KiB | Viewed 429 times ]

Great question. A little slippery. The figure and my diagram are not to scale.
The middle portion, X, is wider than the two squares on the end, though it does not look that way.

1) Find the middle portion's length.

Squares A and B have side length 5 each, total of 10. Rectangle length is 17.
(17 - 10) = 7 = middle region's length

2) Track on where the fold of each square lands (on the diagram, where each square's edge lands is marked in color):

-- When square A is folded over, 7 - 5 = 2 inches remain on the right side of the middle region

So when square B is folded over . . .
B has side length of 5 inches. 2 of those 5 inches will not overlap with A

-- When square B is folded over, 7 - 5 = 2 inches remain on the left side of the middle region

Exactly as above. A has side length of 5 inches
2 of A's 5 inches in length will not overlap with B

3) Area, in square inches, of the part of A that overlaps with B (on diagram, gray area)?

Length of overlap: 7 - 2 - 2 = 3
Area of overlap, L = 3, height is 5:
(3 * 5) = 15

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In the rectangle above, the shaded square regions A and B are to be   [#permalink] 27 Sep 2017, 12:00
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