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Space diagonal of cuboid

  1. Nov 21, 2003 #1


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    im trying to proove that d_abc=(a^2+b^2+c^2)^0.5
    that the space diagonal of a cuboid equals the square root of the sum of the squares of the side lengths.
    here is the picture of cuboid and the diagonals:

    now here's what i did:
    {y}={the part of the space diagonal from the face diagonal d_bc till it touches c}
    {z}={the rest of the sapce diagonal}
    from here im stuck, can someone help me understand what should i do.

    p.s- it's not hw.
  2. jcsd
  3. Nov 21, 2003 #2


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    From pythagorus's theorum, we know that:

    [tex]{d_{ab}}^{ 2} = a^2 + b^2[/tex]

    Also from pythagorus's theroum we known that:

    [tex]{d_{abc}}^2 = {d_{ab}}^2 + c^2[/tex]

    simply substitue the first equation into the second and find the root and you get:

    [tex]d_{abc} = \sqrt{a^2 + b^2 + c^2[/tex]
    Last edited: Nov 21, 2003
  4. Nov 21, 2003 #3


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    PS. the above holds true for any cuboid, a perfect cuboid isonly a special cae where all the edges and diagonals are intergers.
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