What formula represents the perimeter of a rectangle?

The perimeter of a rectangle is the total distance around the shape, which can be calculated using the lengths of its sides. A rectangle has two lengths (l) and two widths (w). Thus, the formula for the perimeter is derived by adding together the lengths and widths twice:

Perimeter = length + width + length + width, which simplifies to Perimeter = 2l + 2w. This can also be factored as 2(l + w), which is the formula you have identified.

This formula captures the necessary components for finding the perimeter of any rectangle, making it essential knowledge in geometry. The other options do not correctly represent the perimeter: simply adding length and width (l + w) provides only half of the required calculation, while lw represents the area, and 2lw is not a standard mathematical formula applicable to the dimensions of a rectangle. The construction of the perimeter formula ensures that both dimensions of the rectangle are considered adequately.