Problem of the Week 1049
If T is an equilateral triangle, then any triangle with the same area and perimeter is congruent to T. This leads to:
True or False: If T is a non-equilateral triangle, then there is a triangle that is not congruent to T but has the same area and perimeter.
Source: Inspired by "A Non-Visual Counterexample in Elementary Geometry" by Marita Barabash, College Math Journal, Nov 2005.
© Copyright 2006 Stan Wagon. Reproduced with permission.