Sunday Times Teaser 2767 – Cutting Corners

by Nick MacKinnon

A cuboidal block has sides that are whole numbers of centimetres, the smallest being of length five and ten centimetres.

A corner is cut off this block to form a triangular face in such a way that each of its sides is the diagonal of a face of the original block. The area of this triangle is a whole number of square centimetres.

What is the length of the longest side of the original block?