A rectangle is a two-dimensional plane quadrilateral, with opposite sides equal and all four angles equal. The perimeter of a rectangle can be defined as the sum of the length of all four sides in a rectangle.

In this article, we are going to learn how to find the perimeter of rectangles using formulas, with the help of examples.

What is Perimeter of Rectangle?

Perimeter of rectangle is the total length of the boundary or the sum of all its sides. In other words, it is the distance around the outside of the rectangle.

Perimeter of Rectangle Formula

Perimeter of Rectangle is the sum of all four sides of Rectangle.

Let us suppose, we take a rectangle of length l and breadth b then its formula for perimeter is given by :

Derivation of Perimeter of Rectangle

It is known the rectangle has 4 sides with two equal sides each, let’s consider the length of one side as ‘l’ and the length of the other side as ‘b’. So there will be l, l, and b, b. So, can deduce the formula for perimeter using the definition of perimeter as follows:

As per perimeter definition, sum of all sides is l + l + b + b = 2l + 2b

So take 2 common, Perimeter = 2(l + b)

Therefore,

Perimeter of a rectangle is 2(l + b)

Perimeter of Rectangle with Diagonal

To find the perimeter of a rectangle when given the length of its diagonal, you can use the relationship between the diagonal, length, and width of a rectangle.

Let’s denote:

• d as the length of the diagonal
• l as the length of the rectangle
• b as the breadth of the rectangle

The relationship between the diagonal and the sides of the rectangle can be expressed using the Pythagorean theorem:

d² = l² + b²

Solving this equation for one of the variables, say l, we get:

l² =d² − b²

Given the length l and breadth b, the perimeter P of the rectangle is:

P = 2l + 2b

Substitute l = √(d² − b²) ​ into the perimeter equation:

P =2 √(d² − b²) + 2b​

This formula gives you the perimeter of the rectangle in terms of its diagonal d and breadth b.

How to Find the Perimeter of Rectangle?

The perimeter of a rectangle can be calculated in a few simple steps. These steps are listed below:

Step 1: For calculating the perimeter of a rectangle, the Length(l) and Breadth(b) of the given figure are noted

Step 2: Values of Length(l) and Breadth(b) are substituted in the formula. P = 2 × (l+b)

Step 3: Solve the formula and the value obtained is the final Perimeter of the given figure.

Perimeter of Rectangle and Square

The formula for the perimeter of a rectangle is:

P​_rectangle =2l + 2b

where l is the length and b is the breadth of the rectangle.

Now, consider a square, which is a special case of a rectangle where all sides are equal. In a square, the length (l) and the breadth (b) are the same. So, we can rewrite the formula for the perimeter of a square as:

P_square ​= 2s + 2s

where s is the length of one side of the square.

This simplifies to:

P_square ​= 4s

Related :

• Rectangle
• Perimeter of Triangle
• Area of Rectangle
• Area of Circle
• Area of Triangle

Solved Examples on Perimeter of Rectangle

Example 1: Find the perimeter of rectangle whose length is 8 cm and breadth is 12 cm.

Solution:

Given, l = 8 and b = 12 cm

So, Substitute both values in perimeter formula,

P = 2(l + b) = 2(12 + 8) = 40 cm

Therefore the perimeter of a rectangle whose length is 8 cm and breadth is 12 cm is 40 cm.

Example 2: Find the perimeter of rectangle whose sides are 2 cm and 4 cm.

Solution:

Given,

l = 2 and another side b = 4 cm.

So, Substitute the both values in perimeter formula,

P = 2(l + b) = 2(2 + 4) = 12 cm

Therefore, the perimeter of a rectangle whose side is 2 cm and another side is 4 cm is 12 cm.

Example 3: Find the perimeter of rectangular carrom board whose sides are 10 cm and 20 cm.

Solution:

Given,

l = 10 and another side b = 20 cm of the carrom board.

So, Substitute the both values in perimeter formula,

P = 2(l + b) = 2(10 + 20) = 60 cm.

Therefore, the perimeter of a rectangular carrom board whose side is 10 cm and another side is 20 cm is 60 cm.

Example 4: Find the perimeter of a bed cot whose sides are 100 cm and 200 cm.

Solution:

Given,

l = 100 and another side b = 200 cm of the bed cot.

So, Substitute the both values in perimeter formula,

P = 2(l + b) = 2(100 + 200) = 600 cm.

Therefore, the perimeter of a bed cot whose sides are 100 cm and 200 cm is 600 cm.

Example 5: Find the perimeter of a compost pit whose longest side is 100 cm and shortest side is 34 cm.

Solution:

Given,

Longest side = 100 cm, so length (l) will be the longest side.

So l = 100 cm. 

Shortest side = 34 cm, so breadth (b) will be the shortest side.

So b = 34 cm 

So, Substitute the both values in perimeter formula,

P = 2(l + b) = 2(100 + 34) = 268 cm

Therefore, the perimeter of a compost pit whose longest side is 100 cm and shortest side is 34 cm is 268 cm

Practice Problems on Perimeter of Rectangle

Q1: Find the perimeter of a rectangular park whose length is 20 m and breadth is 30 m.

Q2: If the length of a rectangle is twice its breadth and the perimeter is 36 m then find the length and breadth of the rectangle.

Q3: If Perimeter of a rectangular field is 30 m and its length is 7 m find its breadth.

Q4: Ram is walking along the boundary of a rectangular field whose length is 20 m and breadth is 60 m. Find the distance covered by Ram in one complete round such that Ram reaches the starting point.

FAQs on Perimeter of Rectangle

What is Perimeter of Rectangle?

The perimeter of a rectangle can be defined as the total distance covered around the boundaries of a rectangle. Simply, the perimeter of a rectangle is its total boundary of it.

Perimeter = 2 × (l + b)

What is Area of Rectangle?

The area of a rectangle is defined as the space that is covered by a rectangle in a 2-D space. Area of a rectangle can also be defined as the number of square units required to completely fill the rectangle.

Area = l × b

How to Find the Perimeter of Rectangle?

Perimeter of a rectangle can be found by adding all the sides of it. Sum of all four sides of the rectangle can is termed its perimeter.

What is Perimeter of Rectangle Formula?

The formula for the perimeter of a rectangle is,

P = 2(l + b)

where, l is length of rectangle, and b is breadth of rectangle.

How To Find the Length of Rectangle, if its Breadth and Perimeter are given?

We know that, the perimeter of a rectangle P = 2(Length + Breadth) units
Thus,
P/2 = Length + Breadth
then, length of a rectangle = {(P/2) – Breadth} units.

Which Unit is used to Measure the Perimeter of Rectangle?

Perimeter of a rectangle is measured in the same unit as the length and breadth of a rectangle, such as cm, m, ft, inches, etc.

How To Find the Perimeter of Rectangle, if its Diagonal is given?

Let “l” is the length and “d” is the diagonal of a rectangle, then breadth can be easily calculated using Pythagoras Theorem and perimeter of rectangle is given by:

P = 2l + 2√(d² – l²) units.