Area and perimeter have different units, so I'll consider only their numeric values. Let the side of the square be S.
The perimeter is 4S and the area is S^2
As the area is 60 more than the perimeter
S^2 - 4S = 60
=> S^2 - 4S - 60 = 0
=> S^2 - 10S + 6S - 60 = 0
=> S(S - 10) + 6(S - 10) = 0
=> (S + 6)(S - 10) = 0
S = -6 and S = 10
As length is positive we eliminate S = -6
The side of the square is 10