Difference between revisions of "2014 AIME I Problems/Problem 1"
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| + | Note that 6 right triangles are formed in the diagram, each with leg lengths <math>50</math> and <math>\frac{80}{3}</math>. By the Pythagoren theorem, the length of each of these hypotenuses is <math>\frac{170}{3}</math>, so the total length minus the two loop pieces is <math>340</math>. Accounting for the two loops, we find that our answer is <math>\boxed{740}</math>. | ||
Revision as of 16:55, 14 March 2014
Problem 1
Solution
Note that 6 right triangles are formed in the diagram, each with leg lengths 
and 
. By the Pythagoren theorem, the length of each of these hypotenuses is 
, so the total length minus the two loop pieces is 
. Accounting for the two loops, we find that our answer is 
.
