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1.问题呈现.如图1,在某条小河L的同一侧有A、B、C三个村庄,它们到小河的距离分别为2km、(?)km、3km,且DE=1km,EF=4.5km;如果在小河L上建一座扬水站向三个村庄供水,那么如何选取扬水站P的位置,才能使铺设的供水管道路程之和最短?2.解法探索.笔者对上述问题探究后发现,该问题可用数理结合的方法来解答.2.1设计一个力学系统(1)根据AD、BE、CF在图1中的位置关系及长度,用刚体材料制成一个框架,再分别于点A、B、C、P处各
1. Problems As shown in Figure 1, there are three villages A, B and C on the same side of a small river L. Their distances from the small river are 2km, (?) Km, 3km, respectively, and DE = 1km, EF = 4.5km; if a water pumping station in the small river L to three villages water supply, then how to choose the location of the pumping station P, in order to make the laying of the water supply pipeline and the shortest sum of 2. Solution .I explore the above problems found , The problem can be solved by mathematical combination method.2.1 Design a mechanical system (1) According to the positional relationship and length of AD, BE, CF in Fig. 1, a frame is made of rigid material, and then at points A, B , C, P at each