Having been given the lengths, *a* and *b*, of two straight lines drawn from the acute angles of a right triangle to the middle of the opposite sides, determine the length of those sides.

*Elements of Geometry*, Benjamin Greenleaf, 1869

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The answer is: the side bisected by \(a\) has length \(2\sqrt{\dfrac{4b^2-a^2}{15}}\), and the side bisected by \(b\) has length \(2\sqrt{\dfrac{4a^2-b^2}{15}}\)