PQRS is a square. By definition of a square, it has 4 equal sides, in this case segments PQ, QR, RS and PS. Based on the given, all segments are equal as proof that PQRS is a square. Furthermore, this square has a units per segment. Thus, all 4 segments measure a units.
SQ is the adjacent side, which cuts the square in triangles.
a^2+a^2=(5√2)^2
hence, a=5 units.
C is the correct answer.
