Faces diagonals

If a cuboid's diagonals are x, y, and z (wall diagonals or three faces), then find the cuboid volume.

Solve for x=1.3, y=1, z=1.2

Correct result:

V =  0.4996

Solution:

x=1.3 y=1 z=1.2  x2=a2+b2 y2=b2+c2 z2=a2+c2  a2=x2b2=x2y2+c2=x2y2+z2a2 2a2=x2y2+z2  a=x2y2+z22=1.3212+1.2221.032   b=x2+y2z22=1.32+121.2220.7906   c=x2+y2+z22=1.32+12+1.2220.6124  V=a b c=1.032 0.7906 0.6124=0.4996



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