2004 AIME I Problem 9

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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.