+327 Let $ABCD$ be a square with side length $1.$ A laser is located at vertex $A,$ which fires a laser beam at point $X$ on side $\overline{BC},$ such that $BX = \frac{1}{2}.$ The beam reflects off the sides of the square, until it ends up at another vertex; at this point, the beam will stop. Find the length of the total path of the laser beam.
+1926 Look at the graph attached below.
The ray will strike X and then, because angle A = angle B it will travel to vertex D
Thus, the total path legnth is
\(2 \sqrt {0 .5^2 + 1^2 } = 2 \sqrt { 5/4} = \sqrt 5\)
Thanks! :)
