WMC 2018 Senior Problem 16

Geometry Level 2

In the city of Sneamc, they play billiards on a rectangular table with dimensions $2.9$ feet by $8.7$ feet. In one game, Mia placed a ball along the shorter edge, $1.3$ feet from a corner. She then hit the ball so that it bounced off each of the other $3$ walls once and returned to its starting point. How many feet did it travel. (Assume the radius of the ball is $0$ ).

6\sqrt{10}

25

24

\frac{32\sqrt{10}}{5}

\frac{29\sqrt{10}}{5}

1 solution

Julian Yu
Oct 20, 2018

As shown in the image, we can reflect the billiards table multiple times so that the distance travelled by the ball (black+red+blue+green) equals the distance from A to A'. By the Pythagorean Theorem, this equals $\sqrt{(2\cdot 2.9)^2+(6\cdot 2.9)^2}=\sqrt{40\cdot 2.9^2}=\frac{29\sqrt{10}}{5}$ .

Note that the fact that the ball was 1.3 feet from a corner was not needed in the solution.

WMC 2018 Senior Problem 16

1 solution

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