Brianna had a garden box in her back yard that is 8 feet by 12 feet. this summer she decides that it is too big and wants to reduce it by a scale factor of 1/2. find the area of her new garden.

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.