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Dimensions of a Triangle
Determine the dimensions for a right-angled triangle, having been given the hypotenuse h, and the side x of the inscribed square (where one vertex of the inscribed square is the right-angled vertex of the triangle).
Elements of Geometry, Benjamin Greenleaf, 1869
Click here to reveal the answer
The answer is: the legs of the right triangle are given by \(\dfrac{x+\sqrt{x^2 + h^2}\pm \sqrt{h^2 - 2x^2 -2x\sqrt{x^2 + h^2}}}{2}\)
"Dimensions of a Triangle," Convergence (March 2006)
