A farmer has a rectangular field that measures 200 meters by 150 meters. He wants to build a triangular irrigation system that covers the entire field. The system will have a right triangle shape, with one leg running along the length of the field, and the other leg running along the width of the field. The hypotenuse will be the pipeline connecting the two ends of the legs. The cost to lay the pipeline along the hypotenuse is $10 per meter, and the cost to lay the pipeline along the legs is $5 per meter. What is the total cost of laying the pipeline for the triangular irrigation system? Let's think step by step and output the final answer within \boxed{}.
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