1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Space diagonal of cuboid

  1. Nov 21, 2003 #1

    MathematicalPhysicist

    User Avatar
    Gold Member

    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:
    http://mathworld.wolfram.com/PerfectCuboid.html

    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}
    y^2=a^2+x^2
    z^2=(c-x)^2+b^2
    z+y=d_abc=(a^2+x^2)^0.5+[(c-x)^2+b^2]^0.5
    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

    jcsd

    User Avatar
    Science Advisor
    Gold Member

    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

    jcsd

    User Avatar
    Science Advisor
    Gold Member

    PS. the above holds true for any cuboid, a perfect cuboid isonly a special cae where all the edges and diagonals are intergers.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook