Find Edge of Cube Given Diagonal

The diagonal of a cube is 20 cm. How long is its edge?


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AG = 20, the diagonal of this beautifully-drawn cube. AG is the hypotenuse of △ACG.
AC = x2, CG = x → AG = √(x2)2 + x2 = √3x2*

So √3x2 = 20 → 3x2 = 400 → x2 = 400/3 →
x = 20/√3x = 20√3/3 ≈ 11.5 cm.

*This is simply the Pythagorean theorem in 3 dimensions: Works for any rectangular solid.

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