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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
Let x be the side of the square.
The area of the square is:
A = x^2
We'll write the formula for the perimeter of the square:
P = 4x
Now, we'll write mathematically the condition imposed by enunciation:
x^2 - 60 = 4x (area is 60 less than the perimeter)
We'll subtract both sides 4x:
x^2 - 4x - 60 = 4x - 4x
We'll eliminate like terms:
x^2 - 4x - 60 = 0
We'll apply the quadratic formula:
x1 = [4+sqrt(16 + 240)]/2
x1 = (4+16)/2
x1 = 10
x2 = (4-16)/2
x2 = -6
Since the length of the side of the square cannot be negative, we'll reject the second root x2 = -6.
The length of the side of the square is x = 10.
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