The perimeter of a rectangle is the distance around the outside of the rectangle. You can find the perimeter of any shape by adding up all of the side lengths of the shape. However, there is an even easier way to find the perimeter of a rectangle because the opposite sides of any rectangle are equal to each other.

\[P=2L+2W\]

## How to Find the Perimeter of a Rectangle

- Find the length and width of the rectangle.
- Plug the length and width into the Perimeter of a Rectangle Formula.

## Examples

*What is the length and width of the rectangle?*

The length of the rectangle is \(\purple l\).

And the width of the rectangle is \(\purple w\).

*What is the perimeter?*

When I plug \(\purple l\) and \(\purple w\) into the perimeter formula, I get…

\[P=2({\purple l})+2({\purple w})\]

When I simplify the expression, I get…

\[P=2L+2W\]

\[P=P\]

The perimeter is \(\purple P\).

*What is the length and width of the rectangle?*

The length of the rectangle is \(\purple l\).

And the width of the rectangle is \(\purple w\).

*What is the perimeter?*

When I plug \(\purple l\) and \(\purple w\) into the perimeter formula, I get…

\[P=2({\purple l})+2({\purple w})\]

When I simplify the expression, I get…

\[P=2L+2W\]

\[P=P\]

The perimeter is \(\purple P\).

*What is the length and width of the rectangle?*

The length of the rectangle is \(\purple l\).

And the width of the rectangle is \(\purple w\).

*What is the perimeter?*

When I plug \(\purple l\) and \(\purple w\) into the perimeter formula, I get…

\[P=2({\purple l})+2({\purple w})\]

When I simplify the expression, I get…

\[P=2L+2W\]

\[P=P\]

The perimeter is \(\purple P\).

## Perimeter of a Parallelogram

The perimeter of a parallelogram is very similar to the perimeter of a rectangle because parallelograms and rectangles both have opposite sides of equal length. You can use the Perimeter of a Rectangle Formula to find the perimeter of a parallelogram as long as you make sure that L and W represent the side lengths of the parallelogram (not the diagonals or perpendicular height).

## Why It Works

The perimeter of any shape is the sum of all of its sides. Rectangles have four sides and the opposite sides are equal to each other. So, the perimeter formula could be written like this:

\[P=l+w+l+w\]

The two \(l\)’s are like terms and so are the two \(w\)’s. When we combine the like terms, we get…

\[P=2l+2w\]