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Geometry · Rectangle · Midpoint · Similar triangles · Right triangle

Problem 2, 2003

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Let \(M\) be the midpoint of the side \(BC\) and \(N\) the midpoint of the side \(CD\) of a rectangle \(ABCD\). Determine the ratio of the side lengths of \(ABCD\), given that \(AMN\) is a right triangle whose hypotenuse is \(AM\).

A B C D N M
The tick marks record that \(N\) and \(M\) are midpoints; the right angle of the triangle lies at \(N\).

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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), izbirno (selection) round 2003, 1. letnik, category A, problem 2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source

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