A question in space geometry

  • Thread starter Chen
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  • #1
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Ok, you take a rectangular and fold it along one of its diagonal, so that the two planes are perpendicular to each other.

Using [tex]a[/tex] and [tex]b[/tex], what is the distance between the points A and B ([tex]d[/tex])?

My anwer is:
[tex]d = \sqrt{a^2 + b^2 - \frac{2a^2b^2}{a^2 + b^2}} = \sqrt{\frac{a^4 + b^4}{a^2 + b^2}}[/tex]
But I doubt that it's actually correct. :)
 

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  • #2
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By the way, this is how I solved it (see attachment). I found x and f with Pythagoras, and using f I found y with the cosine law (the extended Pythagoras thing :wink:). And from there I just used x and y to find d with Pythagoras.

So is this correct, and is there an easier way to do this?
 

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  • #3
verty
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I got the same answer so I am sure it is correct. The only slight difference in what I did was I used the two perpendicular heights and the distance between them.
 

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