We know that
• The area of the floor is 400 square feet.
,• The length is increased by 1 foot each side.
The area of a square is defined as
[tex]A=l^2[/tex]Where A = 400, so
[tex]400=l^2\rightarrow l=\sqrt{400}=20[/tex]Each side is 50 feet long. But, if we increase it as the problem indicates, then each side would be 21, and the area would be
[tex]A=(21)^2=441ft^2[/tex]Therefore, the answer is yes, the area would be a rational number if we increase each side by 1 foot.