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Math Help - Inner diagonals?

  1. #1
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    Question Inner diagonals?

    How do you find inner diagonals of a cube? I was wondering that for a very long time.
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  2. #2
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    Re: Inner diagonals?



    Let a be the length of every side. D'B is an inner diagonal of the cube ABCDA'B'C'D'. B'D, A'C, C'A are also inner diagonals.

    DD' \perp (ABCD), so DD' is perpendicular to DB (since DB is in (ABCD)), that means that BDD' is a right triangle:

    D'D^2+DB^2=D'B^2 \Rightarrow D'B=\sqrt{D'D^2+DB^2}

    ABD is a right triangle, so: AD^2+AB^2=DB^2 \Rightarrow DB^2=2a^2

    D'B=\sqrt{a^2+2a^2}=\sqrt{3a^2}=a\sqrt3
    Last edited by veileen; February 16th 2013 at 11:45 PM.
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