How To Find The Perimeter of a Rectangle

Malcolm McKinsey
Written by
Malcolm McKinsey
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Paul Mazzola

Perimeter of a rectangle

Perimeter of a rectangle is total length of the rectangle's four sides.

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Perimeter of a rectangle formulas

To calculate perimeter of a polygon, add up the lengths of all the straight sides. For a rectangle, that means adding four sides:

Where P is the perimeter and abc, and d are the lengths of the four sides.

Rectangles are interesting, though, because they really have two pairs of two sides; two lengths, and two widths. So instead of writing out P=a+b+c+dP=a+b+c+d you can combine terms and multiply:

Perimeter is always expressed in the same linear measurement used for the lengths of sides.

Perimeter of a rectangle formulas
Perimeter of a rectangle formulas

How to find the perimeter of a rectangle

Here we have a rectangle with four vertices, D, U, C, K.

Rectangle DUCK
Rectangle DUCK

Sides DU and KC are congruent and parallel. Sides DK and UC are also congruent and parallel. That is why you only see two dimensions on the drawing. If Side KC is 17 feet, then you know side DU is 17 feet. Since side DK is 8 feet, you know side UC is 8 feet.

Use either formula:

How to find the perimeter of a rectangle
How to find the perimeter of a rectangle

Let's try the other formula:

See, when calculating the perimeter of DUCK using either formula, you cannot fowl it up!

Perimeter of rectangles example problem

Because the formulas for rectangle perimeter are so easy, they often form the foundation for word problems. Here's one:

Rectangle BRAG
Rectangle BRAG

Rectangle BRAG has a perimeter of 96 cm. Side BR is 3x − 4 long, and side BG is x + 5 wide. What are its measurements?

You can still use either formulas, but you have to simplify along the way.

Combine like terms:

Subtract 2 from both sides:

Finally, divide by 8 and you get your answer:

Now, you can plug 11.75 cm into the x values, and see if you get 96 cm:

And...

Now plug these into the Perimeter formula that we started with:

Do not lose your unit of measure as you work through the problem; all perimeter is measured in the same linear unit you used for each side.