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November 27, 2005
geometrytrapezoidrectanglenumber theoryrelatively prime

Problem Statement

Let ABCABC be a triangle with sides 3, 4, and 5, and DEFGDEFG be a 6-by-7 rectangle. A segment is drawn to divide triangle ABCABC into a triangle U1U_1 and a trapezoid V1V_1 and another segment is drawn to divide rectangle DEFGDEFG into a triangle U2U_2 and a trapezoid V2V_2 such that U1U_1 is similar to U2U_2 and V1V_1 is similar to V2V_2. The minimum value of the area of U1U_1 can be written in the form m/nm/n, where mm and nn are relatively prime positive integers. Find m+nm+n.
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