The area of a square in square feet is represented by z^2+12z+36. 1. find an expression for a side length of the square. 2. find the perimeter when z=12.

1. Find an expression for a side length of the square.
 For this case, the first thing to do is to know that the area of a square is:
 A = L ^ 2
 Where
 L: side of the square.
 We then have to factorize the given polynomial:
 z ^ 2 + 12z + 36
 (z + 6) * (z + 6)
 Rewriting:
 z ^ 2 + 12z + 36 = (z + 6) ^ 2
 
 The side of the square is:
 L = (z + 6)
 2. Find the perimeter when z = 12.
 The perimeter of a square by definition is:
 P = 4L
 Where
 L: side of the square.
 Substituting we have:
 P = 4 (z + 6)
 For z = 12 we have:
 P = 4 (12 + 6)
 P = 72

 
 the perimeter when z = 12 is:
P = 72

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