The front wall of the shed that rita built is 9 feet tall and 5.25 feet wide. after she cut out a section of the door, the area of that wall was 26.25 square feet. the measurements of the doorway were whole numbers of feet. what size is the doorway?

First, we determine the area of the wall before cutting out the door by multiplying the dimensions given. 
                          area of wall = ( 9 ft)(5.25 ft) = 47.25 ft²
Then, we determine the area of the door by subtracting from the total area the area of the remaining wall.
                        area of door = 47.25 ft² - 26.25 ft² = 21 ft²
The two whole numbers that can be the sides of the door are 7 ft x 3 ft.