by H Bradley and C Higgins

A triangle whose side lengths in centimetres are consecutive integers is cut out of a sheet of plywood leaving a hole in it.

To turn the triangle over and fit it back into the hole, it has to be cut into three pieces with two straight cuts, each starting at the midpoint of a side.

Each piece (two having the same perimeter) can then be turned over and put back into its original position in the hole.

What are the lengths of the sides of the original triangle?