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Almost Equilateral Triangles

Problem

We shall define an almost equilateral triangles to be a triangle for which two sides are equal and the third differs by no more than one unit. The smallest such triangle with integral length sides and area is 5-5-6.

Prove that infintitely many almost equilateral triangles with integral length sides and area exist.

Problem ID: 219 (30 Mar 2005)     Difficulty: 4 Star

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