Using pythagorean inequalities, determine which of the following sets of values could represent the lengths of the sides of an obtuse triangle.

a. 11, 12, 22
b. 5, 12, 13
c. 7, 8, 9
d. 5, 6, 1

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.