The diagonal of a cube is 20 cm. How long is its edge?
AG = 20, the diagonal of this beautifully-drawn cube. AG is the hypotenuse of △ACG.
AC = x√2, CG = x → AG = √(x√2)2 + x2 = √3x2*
So √3x2 = 20 → 3x2 = 400 → x2 = 400/3 →
x = 20/√3 → x = 20√3/3 ≈ 11.5 cm.
*This is simply the Pythagorean theorem in 3 dimensions: Works for any rectangular solid.