Geometry · Rhombus · Diagonals · Foot of perpendicular · Right triangles
The rhombus \(ABCD\) has an acute interior angle at the vertex \(A\). The perpendicular dropped from \(D\) to the side \(AB\) meets it at the point \(E\), which splits the side into the two pieces
\[ |AE| = x , \qquad |EB| = y . \]
Express the lengths of both diagonals of the rhombus \(ABCD\) in terms of \(x\) and \(y\).
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), izbirno (selection) round 2005, 1. letnik, category A, problem 4. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source