im trying to proove that d_abc=(a^2+b^2+c^2)^0.5(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Space diagonal of cuboid

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