5. A river runs East to West. Two towns, A and B are, respectively, 4 km and 8 km from the North bank of the river along a straight stretch, as shown in Figure 1. A water pumping station will be built on the bank to serve both towns. Two pipelines will be built; one to connect the pumping station to town A and the other to connect the pumping station to town B. Determine, relative to the point on the riverbank directly South of Town A, the position of the pumping station that will require the minimum amount of pipe and find the total length of pipe required. A 4 km 26 km Figure 1: B 8 km