Perimeter of a Rectangle: Definition, Formula, Derivation, and Examples

Perimeter of Rectangle

 Perimeter of a Rectangle: Perimeter represents the total length of the outer boundary of a closed shape. A defining characteristic of a rectangle is that its opposite sides are equal in length, and every vertex creates a 90-degree angle. Therefore, to calculate the perimeter of a rectangle, you must identify its length and width. Perimeter is typically measured in linear units such as centimeters, meters, inches, or feet.

What is the Perimeter of a Rectangle?

The perimeter of a rectangle is the total distance around its exterior boundary. Mathematically, it is defined as twice the sum of its length and width. It is calculated by summing the lengths of all four sides of the geometric figure.

Perimeter of Rectangle Formula

A rectangle is a quadrilateral with equal opposite sides and four right angles. Since the perimeter is the total sum of all sides, the perimeter of a rectangle is twice the sum of its length and width, represented as follows:

Perimeter = 2 × (Length + Width)

Where, Length = The longer side of the rectangle

Width = The shorter side of the rectangle (also known as breadth)

Derivation of Perimeter of Rectangle 

Since the perimeter of any polygon is the sum of its sides, and a rectangle has two pairs of equal opposite sides, we can derive the formula. If length is 'a' and width is 'b':
So, P = sum of all four sides
Therefore, P = a + b + a + b  (Because opposite sides are equal)
P = 2(a + b)
Hence, the formula is derived.

Calculation of Perimeter of Rectangle

The perimeter of a rectangle is calculated using the following formula:

Perimeter of a rectangle = 2(Length + Width) square units

Perimeter of Rectangle Vs Perimeter of Square

The perimeter of a rectangle differs from that of a square due to their unique side properties—

Perimeter of Rectangle Vs Perimeter of Square
Perimeter of Rectangle	Perimeter of Square
The perimeter of a rectangle is defined as twice the sum of length and breadth, that is, 2(l+b)	The Perimeter of the Square is defined as the sum of all sides, that is, 4(S)
In a rectangle, the opposite sides are equal.	Whereas in Square, all sides are equal.

Perimeter of Rectangle Application

Common real-world applications of calculating the perimeter of a rectangle include:

• In order to calculate the distance covered by walking around a rectangular park.
• In order to measure the length and width of barbed wire required to create a fence around a rectangular plot of land.
• In order to construct the cemented boundary to mark the ground’s total periphery.

Examples of Perimeter of Rectangle

Q1. If a park has a length of 15 meters and a width of 12 meters, what is the perimeter of the rectangle?

Solution: Perimeter of rectangle = 2(l + w)

  Perimeter of Park = 2(15 + 12)

Perimeter of Park = 54 meters

Q2. If a rectangle has a length 'L' and the width is half of the length, calculate its Area and Perimeter.

Solution: According to the problem, length = 'L' and width = 'L/2'. 

Area of the rectangle = Length × Width

Area = L × (L/2) = L²/2

Perimeter of rectangle = 2(l + w)

Perimeter = 2(L + L/2) = 2(3L/2) = 3L

Q3. The area of a rectangular field is 2100 sq. meters. If the field is 60 meters long, what is its perimeter?

Solution: Area of the rectangle = Length × Width

2100 = 60 × Width

Width = 2100 / 60

Width = 35 meters

Perimeter of rectangle = 2(length + width)

Perimeter = 2(60 + 35)

Perimeter = 190 meters