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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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New post 31 Jul 2012, 20:11
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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?
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(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.
Added the diagram.
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Re: Square ABCD has an area of 9 square inches. [#permalink]

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New post 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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New post 31 Jul 2012, 23:50
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(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.

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

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New post 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.

Answer A.

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

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New post 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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