How to find the perimeter of a rectangle? Rectangles are defined by the perimeter of their outer boundaries, which is the total distance between them. Perimeter is twice the sum of the length and width of a rectangle and is calculated using the formula: Perimeter = 2(length + width).

What is the Perimeter of a Rectangle?

The perimeter of a rectangle is the total length of all its sides. A rectangle’s perimeter is measured in linear units of meters, feet, inches, or yards. Let’s start by understanding two of a rectangle’s key properties.

1. All four angles of a rectangle are 90°.
2. Both sides of a rectangle are the same size.

Imagine a rectangular park in your neighborhood. Do you know how long its boundary is?

When you walk around the park’s perimeter once, you cover a lot of ground. This is the park’s perimeter. The perimeter of any rectangular field can be measured by traveling along the boundary of its four sides. Beginning at a fixed point called the starting point, the journey ends when you reach the starting point again. The perimeter of a rectangle is the length or distance of its boundary.

The perimeter of Rectangle Formula

The formula used to calculate the perimeter of a rectangle is the perimeter of a rectangle = 2(l + w), where ‘l’ is the length and ‘w’ is the width of the rectangle. To better understand this, let us look at a simple example. David wants to erect a fence around his farm to prevent his sheep from wandering off. Here is an example of how this formula works. He wants to know how much wire he would need to fence in his rectangular farm.

First, let’s name the sides of his farm. This rectangular farm has a larger side (L). The smaller side is named (W). Adding the distances of all four sides of his farm will give us the perimeter. Total distance = l + w + l + w = 2l + 2w. Therefore, the perimeter of a rectangle = 2(l + w). Here are some examples using this formula.

Examples using Perimeter of Rectangle Formula

Example 1: Calculate the perimeter of a rectangle whose sides are 12 cm and 8 cm.

Solution: Let us find the perimeter of the given rectangle using the perimeter of the rectangle formula, Perimeter of rectangle = 2(l + w). It is given that the length (l) of the rectangle = 12 cm, and width (w) = 8 cm

On substituting the values in the formula, we get, Perimeter of rectangle = 2(l + w) = 2(12 + 8) = 2 × 20 = 40 cm. Therefore, the perimeter of the rectangle is 40 cm.

Example 2: What is the perimeter of a rectangle with a length of 15 m and a width of 9 m?

Solution: Given, Length = 15 m; Breadth (width) = 9 m. We know the formula for the perimeter of a rectangle is: perimeter of rectangle = 2(l + w). Let us substitute the given values which means, P = 2(l + w) = 2(15 + 9) = 2 × 24 = 48 m. Therefore, the perimeter of the indicated rectangle is 48 m.

The perimeter of Rectangle Formula vs Perimeter of Square Formula

The perimeter formula for a rectangle is different from the perimeter formula for a square.

• The perimeter of a rectangle formula is expressed as Perimeter of rectangle = 2(l + w); where ‘l’ is the length and ‘w’ is the width. However, the perimeter of a square formula is expressed as, the perimeter of a square = 4 × s; where ‘s’ is the side length.
• Rectangle perimeter formula differs from square perimeter formula because only the opposite sides of a rectangle are equal. However, in the case of a square, all the sides are of equal length.

Relationship Between Area and Perimeter of a Rectangle

A rectangle’s area and perimeter do not have a direct relationship. This is because the perimeter of a rectangle is the total length of its boundary and is expressed in linear units like cm, inches, and so on. The perimeter of a rectangle formula = 2(length + width). On the other hand, the area of a rectangle is the total space occupied by the rectangle and is expressed in square units like cm², inches², and so on. The formula for the area of a rectangle is Area of rectangle = length × width

How to Find the Perimeter of a Rectangle?

In three simple steps, we can calculate the perimeter of a rectangle. Listed below are the steps to calculate the perimeter.

• In order to calculate the perimeter of a rectangle, the length and width must be known.
• The length and width values are substituted into the formula.
• After solving the equation, the perimeter value is calculated.

The formula used to calculate the perimeter of a rectangle is:

The perimeter of a rectangle = 2(l + w); where ‘l’ is the length and ‘w’ is the width of the rectangle.

In other cases, only the perimeter of a rectangle is known, but the other dimensions are not. We use the following formulas:

• When the perimeter and length of a rectangle are known, the width can be calculated using the formula: Width = P/2 – l, where l = length of the rectangle; and w = width of the rectangle, and P = perimeter of the rectangle.
• Similarly, if the perimeter and width of the rectangle are known, the length can be calculated using the formula: Length(L) = P/2 – w. Where P = perimeter of the rectangle; and w = width of the rectangle.

Usage of Perimeter of a Rectangle

Our everyday lives are made easier by calculating distances and lengths using the perimeter of a rectangle.

For example,

• If you need to decorate the border of your rectangular notebook, you can easily calculate how much ribbon you would require by finding the perimeter.
• If you need to put a fence around your garden, the perimeter of the garden will give you the exact length of wire you would require.