Perimeter = (3+3)*(N-50)     (1)     ("If the pickets were placed 3 inches apart, 50 pickets are left ove")
Perimeter = (3+2.5)*(N+50)   (2)     ("If pickets are placed 2.5 inches apart, 50 more are needed")

                                     (Notice that in (1) 3+3 is the distance between "axial lines" of the pickets: 
                                      3 in is their width and 3 in is the distance between them)
                                     (same meaning has 3+2.5 in the equation (2) )

==============>  6*N - 300 = 5.5*N + 275,

6N - 5.5N = 300 + 275,

0.5N = 575  ====>  N = 1150.


So, N = 1150 pickets were purchased.


Then the perimeter = 6*(N-50) = 6*1100 = 6600 inches.


Hence, the side of the square =  = 1650 inches,


Then the area = 1650^2 = 2722500 sq. inches =  sq. ft = 18906.25 sq. ft.