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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.

 Apr 30, 2024
 #1
avatar+128772 
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The ray will strike X  and then , because angle A = angle B  it will travel to  vertex D

 

The  total path length =   2 sqrt [ .5^2  + 1^2 ] =  2 sqrt [ 5/4]  = sqrt 5

 

 

cool cool cool

 Apr 30, 2024

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