Perimeter of Rectangle

The perimeter of any given rectangle is a fundamental concept in geometry that refers to the total distance around a rectangle. It can be calculated by adding up the lengths of all four sides. It is expressed in linear units of meters, feet, inches, or yards.  

The formula for finding the perimeter of a rectangle has important real-life applications in measuring the amount of fencing needed for a yard, calculating the length required for a picture frame.

1.0Understanding the Perimeter of a Rectangle

Perimeter refers to the continuous line that forms the boundary of a closed geometric figure. Therefore, the perimeter of a rectangle is the distance covered by the boundaries of the four sides present in the rectangle. Since the opposite sides of every rectangle are equal, the formula for the perimeter of a rectangle would be:

P = 2 × (l + w)

Here, “P” denotes the total perimeter, “l” denotes the length of the rectangle and “w” denotes the width of the rectangle. Utilising the formula, you can easily calculate the perimeter of a rectangle for different purposes.

2.0Examples to Find the Perimeter of a Rectangle

Let’s look at a few examples to see how you can apply the formula for the perimeter of a rectangle in mathematical and real-life problems.

Example: A garden has a length of 10 meters and a width of 5 meters. Find how much fencing the garden needs.

Solution:

Perimeter, P = 2(length + width)

P = 2 × (10 + 5)

P = 2 × 15 

P = 30 meters

You will need 30 meters of fencing for the garden. 

Example: A rectangular swimming pool has a perimeter of 64 meters. If its width is 12 meters, what is its length?

We use the formula:

P = 2 × (l + w)

Substituting the values:

64 = 2 × (l + 12)

Dividing by 2:

32 = l + 12 

Solving for l =

l = 32 − 12 = 20 meters 

The length of the pool is 20 meters.

Example: Aman wants to fence his garden with dimensions as length equal to 10 meters and a width of 300 centimetres. Find out how much wire is required (in centimetres) to fence Aman’s garden.

Solution:

Given that, length = 10m and width of garden = 300cm 

Length of garden in centimetres = 10100 = 1000cm 

Perimeter, P = 2(length + width)

P=2×(1000+300) = 2×1300 =2600 cm 

Therefore, the fence required for the garden is 2600 cm. 

Example: Finding Width from Perimeter

A rectangular garden has a perimeter of 150 feet. If its length is 45 feet, find the width.

Solution:
Using the perimeter formula:

150 = 2×(45 + w)

Dividing by 2:

75 = 45 + w

Solving for w:

w = 75 − 45 = 30 feet 

Answer: The width of the garden is 30 feet.

3.0Comparing the Area and Perimeter of a Rectangle Formula

Many students get confused between the formula of the perimeter and the area of a rectangle. The area and perimeter of the rectangle formula are inherently different. The perimeter of rectangle formula in maths calculates the total length of the boundary, whereas the area of a rectangle calculates the total space covered within the boundaries of the rectangle. Refer to the table below to understand the key differences between the area and perimeter of rectangle formula. 

4.0Real-Life Applications of the Perimeter of a Rectangle

There are many real-life applications for the perimeter of rectangle formula in maths. It is utilised regularly in construction, home improvement, and land surveying. 

• Construction and Architecture

In construction and architecture, the formula for perimeter of a rectangle is used to calculate the length of the walls, borders, and fences required for a structure. It also gives an idea about the amount of material needed for the project.

• Home Improvement

Homeowners use perimeter calculations for a myriad of things like installing baseboards, garden fencing, carpeting the edges of a room, etc. 

• Gardening

In gardening, understanding the perimeter is vital for the proper design of the layout. The formula for perimeter of a rectangle not only allows you to understand the layout of flower beds, vegetable patches, and walking paths but also determines the amount of seeds and fertilisers needed for your garden.

• Arts and Crafts

In arts and crafts, perimeters are used to understand the borders and frames needed for a piece. You can easily get the size of the frame needed by measuring the length and the width to calculate the perimeter. 

5.0Common Mistakes While Calculating the Perimeter of a Rectangle

A common mistake made by students is confusing between the area and the perimeter of a rectangle. The area of a rectangle refers to the amount of space covered by the four sides, and the perimeter of a rectangle refers to the boundary of the rectangle. 

Many students make unit conversion errors in the examination. If the length and the width are given in different units, one needs to convert them to the same unit before calculation. For example, if the length of the rectangle is in centimetres and the width of the rectangle is in meters, you need to convert both in either centimetres or meters before the perimeter calculation.

The formula for perimeter of a rectangle is P = 2(l + w). Many students forget to multiply the length and the width by 2. As the rectangle has two pairs of equal sides, this leads to a grave calculation error. 

6.0Conclusion

With this knowledge, you can definitely calculate perimeter of a rectangle and solve many mathematical and real-life problems. Keep practising related problems with different values and scenarios to become adept at them.