Question 1028619
Let the side length of the square be s. The triangular regions outside the square are all isosceles right triangles, so you can work out that there are many segments of side length s. In particular, the two vertices of the square trisect the hypotenuse, and the length of the hypotenuse is s+s+s = 3, or s = 1.


It is a little difficult to explain in words, but draw it out and you should figure it out.