Consider two functions, \( f(x) = \sqrt{x} + 3 \) and \( g(x) = x^2 - 4 \). If the perimeter of a rectangle is given by \( P = 2l + 2w \), where \( l \) and \( w \) are the length and width respectively, and we know \( l = f(16) \) and \( w = g(2) \), find the perimeter of the rectangle. Let's think step by step and output the final answer within \boxed{}.
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