1986 AHSME Problems/Problem 19
Problem
A park is in the shape of a regular hexagon km on a side. Starting at a corner, Alice walks along the perimeter of the park for a distance of km. How many kilometers is she from her starting point?
Solution
We imagine this problem on a coordinate plane and let Alice's starting position be the origin. We see that she will travel along two edges and then go halfway along a third. Therefore, her new -coordinate will be because she travels along a distance of km because of the side relationships of an equilateral triangle, then km because the line is parallel to the -axis, and the remaining distance is km because she went halfway along and because of the logic for the first part of her route. For her -coordinate, we can use similar logic to find that the coordinate is . Therefore, her distance is giving an answer of .
See also
1986 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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