+478 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.
+1950 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√0.52+12=2√5/4=√5
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