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# Square ABCD has an area of 9 square inches. Sides AD and BC

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Square ABCD has an area of 9 square inches. Sides AD and BC [#permalink]

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31 Jul 2012, 20:11
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76% (02:01) correct 24% (00:43) wrong based on 81 sessions

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Square ABCD has an area of 9 square inches. Sides AD and BC are lengthened to x inches each. By how many inches were sides AD and BC lengthened?
Attachment:

Square.png [ 5.13 KiB | Viewed 3017 times ]

(1) The diagonal of the resulting rectangle measures 5 inches.
(2) The resulting rectangle can be cut into three rectangles of equal size.

Can anyone help me vvith B please .. Ive got A right
[Reveal] Spoiler: OA

Last edited by Bunuel on 01 Aug 2012, 03:47, edited 1 time in total.
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Re: Square ABCD has an area of 9 square inches. [#permalink]

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31 Jul 2012, 23:01
Edit: never mind I thought it was a rectangle instead of a square, deleted my post to avoid confusion, I keep my explanation of statement 2 since it is mentioned by someone else below.

2) Any rectangle can be divided into 3 rectangles of equal size, insufficient

Last edited by duriangris on 01 Aug 2012, 00:40, edited 1 time in total.
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Re: Square ABCD has an area of 9 square inches. [#permalink]

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31 Jul 2012, 23:50
1
KUDOS
(1) Given that the area of the square is 9, then each side of the square is 3.
The lengthened sides will be of length 3 + x each, and the diagonal of the obtained rectangle being 5,
we can write $$(x+3)^2+3^2=5^2$$, from which $$(x+3)^2=16$$, so $$x = 1$$.
Sufficient.

(2) Obviously, not sufficient, as was already mentioned by "duriangris" in the previous post.

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Manager
Joined: 22 Jun 2012
Posts: 53
GMAT 1: 730 Q49 V40
Followers: 2

Kudos [?]: 18 [0], given: 6

Re: Square ABCD has an area of 9 square inches. [#permalink]

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01 Aug 2012, 00:38
EvaJager wrote:
(1) Given that the area of the square is 9, then each side of the square is 3.
The lengthened sides will be of length 3 + x each, and the diagonal of the obtained rectangle being 5,
we can write $$(x+3)^2+3^2=5^2$$, from which $$(x+3)^2=16$$, so $$x = 1$$.
Sufficient.

(2) Obviously, not sufficient, as was already mentioned by "duriangris" in the previous post.

Gosh! it was a square not a rectangle!!
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Re: Square ABCD has an area of 9 square inches. Sides AD and BC [#permalink]

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07 Jan 2016, 21:04
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Re: Square ABCD has an area of 9 square inches. Sides AD and BC   [#permalink] 07 Jan 2016, 21:04
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