2014 AIME I Problems/Problem 1

Problem 1

Solution

Note that 6 right triangles are formed in the diagram, each with leg lengths $50$ and $\frac{80}{3}$ . By the Pythagoren theorem, the length of each of these hypotenuses is $\frac{170}{3}$ , so the total length minus the two loop pieces is $340$ . Accounting for the two loops, we find that our answer is $\boxed{740}$ .

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2014 AIME I Problems/Problem 1

Problem 1

Solution