Question

Let ABCDEFGH be a cube and M the midpoint of GH. It is known that the distance between the lines BM and AD is a
`√(5)`. What is the length of AB?

Answer 1

√5

Explanation:

We suppose the vertices are named clockwise around the top of the cube, then clockwise around the bottom (looking down from above the cube), with vertex E below vertex D. Then line AD is in plane ADEF, and line BM is in plane BCHG.

The distance between the named parallel planes is the distance between the lines. That distance is AB, which is given as √5.

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A diagram helps.