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Two Equal Parts of a Triangle

The three sides of a triangular piece of land, taken in order, measure 15, 10, and 13 chains respectively; it is required to divide it into two equal parts by a line constructed parallel to the second side.  What will be the length of the division line and its distance from the place of beginning, measured on the first side?

A Treatise on Surveying, John Gummere, 1817

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"Two Equal Parts of a Triangle," Convergence (July 2006)