Sunday Times Teaser 2767 – Cutting Corners
by Nick MacKinnon
Published: 4 October 2015 (link)
To make an unusual paperweight a craftsman started with a cuboidal block of marble whose sides were whole numbers of centimetres, the smallest sides being 5cm and 10cm long. From this block he cut off a corner to create a triangular face; in fact each side of this triangle was the diagonal of a face of the original block. The area of the triangle was a whole number of square centimetres.
What was the length of the longest side of the original block?