Mr. Reed is drawing a blueprint of a rectangular patio. The width of the patio is 4034 feet shorter than twice its length. The perimeter of the patio is 8612 feet. What is the length of the patio? Let represent the length of the patio. Select the correct values to write an equation to represent the situation.

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.