PUZZLET 062

A Scalene Triangle

A triangle has integer sides of consecutive lengths. It is scalene, since all sides are of different lengths.

If a line is drawn at right angles from the medium-length side to the opposite vertice, it will have an integer value one less than the shortest side's length.

What are the least lengths of the sides and line of the triangle as described? Note: the drawing isn't to scale.

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Last Updated: January 12th, 2010.