Length and Width of a Rectangle given Perimeter Calculator

Created by Adena Benn
Reviewed by Krishna Nelaturu
Last updated: Mar 14, 2022

Our length and width of a rectangle given perimeter calculator will help you calculate the unknown side of any rectangle. If you are looking to find the width of a rectangle and already know the perimeter, you have come to the right place. We will share:

  • How to find the unknown sides of a rectangle when the only thing you know is the perimeter.
  • How to find the length of a rectangle given the perimeter and the width.
  • The length of a rectangle formula.
  • The relationship between a square and a rectangle.

🔎 Since a square has all the properties of a rectangle, we say a square is a type of rectangle. However, not all rectangles are squares.

How to find the length and width of a rectangle given the perimeter

Generally, if you are given the perimeter of a rectangle and asked to find the length and width, this would be impossible unless the rectangle also happens to be a square. Because all the sides of a square are equal, finding both length and width would be possible.

The formula for the perimeter of a square is: P = 4X, where X is the unknown sides, and P is the perimeter. So to find the width of a square, we would make X the subject of the formula. Our new formula would then read X = P/4.

Find the length of a rectangle given the perimeter

We use a different formula where the rectangle is not also a square. We will need to know the measurement of at least one side. The required inputs are also different. We use one of the following equations for the perimeter of a rectangle.

P = 2(L + W) or P = 2 × L + 2 × W

So using the first equation for the perimeter of a rectangle, let's assume the length of a rectangle is unknown, but you know the perimeter and the width. You then make the unknown value the subject of the formula. The new equation created is our length of rectangle formula. So, from the first formula above, we would get the following equation. It is the formula used by our length and width of a rectangle given perimeter calculator:

  • L = (P/2) - W

To find the width of the rectangle, you would make W the subject of the formula instead.

To use this length and width of a rectangle given the perimeter calculator, we need to input the perimeter and the value of one side.

Let's look at this example: The perimeter of a rectangle is 10 inches, and the width is 3 inches.

Using the formula: L = (P/2) - W

Substitute in the known values:

  • L = 10 / 2 - 3
  • L = 5 - 3 = 2.

Be sure to check out these related calculators:

Adena Benn
Perimeter
in
Length
in
Width
in
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