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)