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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