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Square ABCD is the base of the cube while square EFGH is the

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Re: Square ABCD is the base of the cube while square EFGH is the  [#permalink]

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New post 05 Mar 2018, 07:18
Bunuel wrote:
ayush98 wrote:
Bunuel wrote:
Square ABCD is the base of the cube while square EFGH is the cube's top facet such that point E is above point A, point F is above point B etc. What is the distance between the midpoint of edge AB and the midpoint of edge EH if the area of square ABCD is 2?

A. \(\frac{1}{\sqrt{2}}\)
B. 1
C. \(\sqrt{2}\)
D. \(\sqrt{3}\)
E. \(2\sqrt{3}\)

Look at the diagram below:
Attachment:
Cube.png
Notice that Z is the midpoint of AD. We need to find the length of line segment XY.

Now, since the area of ABCD is 2 then each edge of the cube equals to \(\sqrt{2}\).

\(XZ=\sqrt{AX^2+AZ^2}=\sqrt{(\frac{\sqrt{2}}{2})^2+(\frac{\sqrt{2}}{2})^2}=1\);
\(XY=\sqrt{XZ^2+YZ^2}=\sqrt{1^2+(\sqrt{2})^2}=\sqrt{3}\).

Answer: D.


How do we know that XZ is 1 ?


Please tell me what to elaborate here: \(XZ=\sqrt{AX^2+AZ^2}=\sqrt{(\frac{\sqrt{2}}{2})^2+(\frac{\sqrt{2}}{2})^2}=1\)?


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Re: Square ABCD is the base of the cube while square EFGH is the  [#permalink]

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New post 18 Jun 2019, 00:20
bmwhype2 wrote:
Square ABCD is the base of the cube while square EFGH is the cube's top facet such that point E is above point A, point F is above point B etc. What is the distance between the midpoint of edge AB and the midpoint of edge EH if the area of square ABCD is 2?

A. \(\frac{1}{\sqrt{2}}\)
B. 1
C. \(\sqrt{2}\)
D. \(\sqrt{3}\)
E. \(2\sqrt{3}\)

m14 q23


Please find teh solution as attached

Answer: Option D
Attachments

Screenshot 2019-06-18 at 12.49.48 PM.png
Screenshot 2019-06-18 at 12.49.48 PM.png [ 265.37 KiB | Viewed 54 times ]


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Re: Square ABCD is the base of the cube while square EFGH is the   [#permalink] 18 Jun 2019, 00:20

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