Perimeter of Rectangle: Definition, Formula, Derivation & Examples

Perimeter of Rectangle

 Perimeter of Rectangular: Perimeter is basically the length of the enclosed space. It is the sum of all the sides of the boundary. One of the distinguishing characteristics of the rectangle is that the opposite sides of the rectangle are the same and each vertex forms a 90-degree angle.  So it is necessary to find the dimension of length and breadth in order to find out the perimeter of the rectangle. The Perimeter can be measured in centimeters, meters, inches, feet, etc.

What is the Perimeter of a Rectangle?

The perimeter of a rectangle is defined as the total distance of its outer boundary. Mathematically, it is twice the sum of its length and width. It is calculated by covering the total path of the geometrical shape.

Perimeter of Rectangle Formula

The rectangle is a type of irregular polygon that has only equal opposite sides equal but the angle formed is equal in all measures. As we know, the perimeter is the sum of all the sides. So the perimeter of the rectangle is twice the sum o length and breath, that is,

Perimeter = 2( Length + breadth)

Where, Length = Length of the rectangle

Breadth = Breadth of the rectangle

Derivation of Perimeter of Rectangle 

Since the perimeter of the polygon is equal to the sum of all the sides and the rectangle is an irregular polygon having two opposite sides. In Rectangle, the length is ‘a’ and the breath is ‘b’.
So, P = sum of all its four sides
Hence, P = a + b + a + b  (Opposite sides of a rectangle are equal)
P = 2(a + b)
Hence derived.

Calculation of Perimeter of Rectangle

The perimeter of the rectangle is calculated by using the formula:

Perimeter of Rectangle Vs Perimeter of Square

The perimeter of the Rectangle is not similar to the Perimeter of the Square. There is a difference between them-

Perimeter of Rectangle Application

The application of the Perimeter of the Rectangle is -

• 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 the length of the park is 15 meters and the breadth of the park is 12 meters. Calculate the perimeter of the rectangle.

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

  Perimeter of Park = 2 (15 + 12)

Perimeter of Park = 54 Units

Q2. If a rectangle has a length ‘L’ and the width is one-half of the length. Then Calculate the Area and Perimeter of the rectangle.

Solution: According to the question, length is ‘L’ and width is ‘L/2’. 

Then the area of the rectangle = L × B

Area = L × L/2 = L² /2 

Perimeter of rectangle= 2( l+b)

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

Q3. The area of the rectangle field is 2100 sq. meters. If the field is 60 meters long. What is its perimeter?

Solution: Area of the rectangle = L × B

2100 = 60 × B

B = 2100/60

B = 35 meters.

Perimeter of rectangle= 2( l+b)

Perimeter of rectangle = 2( 60 + 35)

Perimeter of rectangle = 190 Units