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Distance problem

Source: AHSME 1986 problem 19

October 1, 2011
geometryperimeteranalytic geometryAMC

Problem Statement

A park is in the shape of a regular hexagon 22 km on a side. Starting at a corner, Alice walks along the perimeter of the park for a distance of 55 km. How many kilometers is she from her starting point?
<spanclass=′latex−bold′>(A)</span> 13<spanclass=′latex−bold′>(B)</span> 14<spanclass=′latex−bold′>(C)</span> 15<spanclass=′latex−bold′>(D)</span> 16<spanclass=′latex−bold′>(E)</span> 17 <span class='latex-bold'>(A)</span>\ \sqrt{13}\qquad<span class='latex-bold'>(B)</span>\ \sqrt{14}\qquad<span class='latex-bold'>(C)</span>\ \sqrt{15}\qquad<span class='latex-bold'>(D)</span>\ \sqrt{16}\qquad<span class='latex-bold'>(E)</span>\ \sqrt{17}
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