Final answer:
The perimeter of a rectangle as a function of its side length l, given an area of 16 m², is P = 2l + 32 / l. The options provided in the question do not match the correct expression for the perimeter.
Step-by-step explanation:
To find the perimeter of the rectangle as a function of the length of one of its sides, let's call the length of the side l and the width w. We know that the area A of a rectangle is the product of its length and width, i.e., A = l × w. Given that the area is 16 m², we can express the width in terms of the length as w = 16 / l.
The perimeter P of a rectangle is the sum of twice its length and twice its width, so P = 2l + 2w. Substituting the expression for width we found earlier, we get P = 2l + 2(16 / l), which simplifies to P = 2l + 32 / l. However, none of the given options matches this expression. Therefore, either the given options are incorrect, or there may have been a misunderstanding in the formulation of the options.