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# In the rectangle shown above, a, b, c, and d are the length

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Manager
Joined: 16 Feb 2011
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In the rectangle shown above, a, b, c, and d are the length  [#permalink]

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14 Aug 2011, 12:03
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Difficulty:

65% (hard)

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50% (02:17) correct 50% (01:53) wrong based on 36 sessions

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In the rectangle shown above, a, b, c, and d are the length of the corresponding line segment. In terms of b, c, and d, a^2 = ?

(A) b^2 + d^2 + c^2
(B) b^2 - d^2 + c^2
(C) b^2 + d^2 - c^2
(D) d^2 - b^2 + c^2
(E) b^2 - c^2 - d^2

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Wierd Geometry.docx [14.4 KiB]

Senior Manager
Joined: 03 Mar 2010
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Schools: Simon '16 (M\$)
Re: In the rectangle shown above, a, b, c, and d are the length  [#permalink]

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14 Aug 2011, 12:38
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$$b^2 = m^2+x1^2$$
$$c^2 = m^2+x2^2$$
Subtracting,
$$b^2-c^2=x1^2-x2^2$$ ---(1)

Also,
$$p^2=a^2-x1^2=d^2-x^2$$
$$a^2=d^2+x1^2-x^2$$
From 1, $$x1^2-x2^2 = b^2-c^2$$
$$a^2 = d^2+b^2-c^2$$
$$a^2 = b^2+d^2-c^2$$

OA C.
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Re: In the rectangle shown above, a, b, c, and d are the length  [#permalink]

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14 Aug 2011, 19:13
assume this as a cuboid and we were only shown the front face of the cuboid .

we should see two right angled triangles.

a^2= b^2+h^2

d^2 = c^2+h^2

where h is the height of the front face of the rectangle.
a,b,c and d are all the diagonals connecting different corners of the cuboid.

using the above two equations we can eliminate h^2

=> a^2 = b^2+d^2-c^2

Director
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Re: In the rectangle shown above, a, b, c, and d are the length  [#permalink]

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14 Sep 2011, 07:11
I do not think this is gmatprep questions. gmatprep questions are basic though they can be hard.
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Re: In the rectangle shown above, a, b, c, and d are the length  [#permalink]

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15 Sep 2011, 07:44
DeeptiM wrote:
Is there any easy way to underdtand & solve such questions?

In the rectangle shown above, a, b, c, and d are the length of the corresponding line segment. In terms of b, c, and d, a^2=?
(A) b^2+d^2+c^2
(B) b^2-d^2+c^2
(C) b^2+d^2-c^2
(D) d^2-b^2+c^2
(E) b^2-c^2-d^2

If this question has a unique answer, the answer must be correct no matter how we draw the diagram. So we can imagine the diagram drawn in either extreme or completely symmetric ways to work out what the answer must be. For example, it's certainly possible that the diagram is a square, and that our two diagonals cut each other in half. In that case, a, b, c and d would all be equal. So we can rule out answers A (much too large) and E (which would be negative).

The most useful diagram to imagine is one where the four lines intersect at the bottom right corner of the rectangle. Then a is just a diagonal of the rectangle, b is just the base, d is just the height, and c = 0. Since then it's clear from Pythagoras that b^2 + d^2 = a^2, the answer must be C.
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WE: Information Technology (Computer Software)
Re: In the rectangle shown above, a, b, c, and d are the length  [#permalink]

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15 Sep 2011, 10:45
OA is C. My method was similar to jamifahad.
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Re: In the rectangle shown above, a, b, c, and d are the length  [#permalink]

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22 Mar 2019, 01:26
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Re: In the rectangle shown above, a, b, c, and d are the length   [#permalink] 22 Mar 2019, 01:26
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# In the rectangle shown above, a, b, c, and d are the length

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