Hosted by The Math Forum## Problem of the Week 1049## Twin Triangles
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, © Copyright 2006 Stan Wagon. Reproduced with permission. |

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6 February 2006