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

Question

Untitled.png 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

jamifahad · Answer

Screen Shot 2011-08-14 at 10.29.37 PM.png 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.

Spidy001 · Answer

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.

thangvietname · Answer

I do not think this is gmatprep questions. gmatprep questions are basic though they can be hard.

IanStewart · Answer

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.

reatsaint · Answer

OA is C. My method was similar to jamifahad.

bumpbot · Answer

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

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

Prep Toolkit

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