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655-705 (Hard)|   Geometry|      
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DeeptiM
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In the rectangle shown above, a, b, c, and d are the length 14 Aug 2011, 12:03
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

65% (hard)

Question Stats:

50% (02:15) correct 50% (02:01) wrong based on 52 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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C

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jamifahad
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In the rectangle shown above, a, b, c, and d are the length 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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In the rectangle shown above, a, b, c, and d are the length 14 Aug 2011, 19:13
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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

Answer is C.
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In the rectangle shown above, a, b, c, and d are the length 14 Sep 2011, 07:11
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I do not think this is gmatprep questions. gmatprep questions are basic though they can be hard.
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In the rectangle shown above, a, b, c, and d are the length 15 Sep 2011, 07:44
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DeeptiM
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
Show more

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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In the rectangle shown above, a, b, c, and d are the length 15 Sep 2011, 10:45
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OA is C. My method was similar to jamifahad.
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In the rectangle shown above, a, b, c, and d are the length 22 Mar 2019, 01:26
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