### by H Bradley and C Higgins

#### Published: 2 October 2011 (link)

Pat likes to demonstrate his favourite trick shot on the pub pool table, which is 90in long and 48in wide.

Pat hits the ball so that it strikes the long side of the table first, then (after a perfect bounce) it hits the short side, then the other long side, and then finally the other short side, from which it returns to the starting point, making its path the perimeter of a quadrilateral.

What is the length of the perimeter of that quadrilateral?

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Hence the length of the path travelled by the ball is given by $2\sqrt{w^2+h^2}$. In our case this becomes $2\sqrt{48^2+90^2}=12\sqrt{8^2+15^2}$ This is easily recognised as the Pythagorean triple $$(8, 15, 17)$$, which shows that the path length is 204cm.