Let \(ABC\) be a triangle with sides 3, 4, and 5, and \(DEFG\) be a 6-by-7 rectangle. A segment is drawn to divide triangle \(ABC\) into a triangle \(U_1\) and a trapezoid \(V_1\) and another segment is drawn to divide rectangle \(DEFG\) into a triangle \(U_2\) and a trapezoid \(V_2\) such that \(U_1\) is similar to \(U_2\) and \(V_1\) is similar to \(V_2.\) The minimum value of the area of \(U_1\) can be written in the form \(m/n,\) where \(m\) and \(n\)are relatively prime positive integers. Find \(m+n.\)
(第二十二届AIME1 2004 第9题)