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} + *x*^{2} = √3*x*^{2}^{*}

So √3*x*^{2} = 20 → 3*x*^{2} = 400 → *x*^{2} = 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.