Problem of the Week 1049

Twin Triangles

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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.