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Let l be the length of the side of the square. We can relate this problem to picking a random point, (A,B) from a 1x1 square (so l = 1). The length of the line segment AB is given by .

Here we see that and every point is equally likely. Using the hint, we have

Problem 14

References: Mathematics Magazine, Philip W. Kuchel and Rodney J. Vaughn, "Average Lengths of Chords in a Square"