Ontario Mathematics Proficiency Practice Test

The formula for the perimeter of a rectangle is derived from the definition of perimeter itself, which is the total distance around the figure. A rectangle has two lengths and two widths.

To calculate the perimeter, you add the lengths and the widths together, which can be represented as:

1. Start with the lengths: \( l + l = 2l \)

2. Next, add the widths: \( w + w = 2w \)

Now, combine these results to obtain the total perimeter:

\[

P = 2l + 2w

\]

This can be factored as:

\[

P = 2(l + w)

\]

Thus, the expression accurately represents the total distance around the rectangle. This is why the correct option is the expression for the perimeter of a rectangle given its length and width. Other provided options do not align with this understanding; for instance, simply adding the length and width does not account for all sides of the rectangle, leading to insufficient representation of the perimeter. Similarly, the other formulas either represent area or miss essential components of calculating perimeter.