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Perimeter of Rectangle: Definition, Formulas, Solved Examples

The perimeter of a rectangle is the total length of its boundary, made up of two equal longer sides and two equal shorter sides. Learn steps to calculate the perimeter of a rectangle with solved examples here.

Chandni 2 Jan, 2025

Perimeter of Rectangle: Suppose you are helping your family build a vegetable garden in the backyard. To keep it safe from animals, you need to fence it completely.

But how much fencing material should you buy? The answer lies in calculating the perimeter of the rectangle, which is the total distance around its boundary. This simple yet practical concept plays a key role in many real-life scenarios. In this blog post, we will explore the basics of the perimeter of a rectangle, how to calculate it, and its various applications in daily life. [video width="1920" height="1080" mp4="https://www.pw.live/exams/wp-content/uploads/2024/12/Curious-Jr-Ad-3-1-1.mp4"][/video]

What is a Rectangle?

A rectangle is a two-dimensional quadrilateral with opposite sides that are equal in length and parallel. All four interior angles measure exactly 90 degree, making it an equiangular quadrilateral. The longer side is referred to as the length, while the shorter side is called the width. Additionally, the diagonals of a rectangle are equal in length and intersect at their midpoints, bisecting each other. T hese properties make the rectangle a fundamental shape in geometry, widely used in everyday applications and mathematical studies.

Vertical Line

What is the Perimeter of a Rectangle?

The perimeter of a rectangle is the total distance around its sides. To find it, start at one corner and count the units along each side until you get back to where you started. For example, suppose a rectangle has sides measuring 9 units and 3 units.

Adding the lengths of all four sides of the given rectangle gives: 9 + 3 + 9 + 3 = 24 units Thus, the perimeter of the rectangle is 24 units. Alternatively, since opposite sides of a rectangle are equal, you can simplify the calculation by multiplying each pair of sides by 2 and then adding: (9×2) + (3×2) = 18 + 6 = 24 units. In both methods, the perimeter of the rectangle is 24 units. [video width="1920" height="1080" mp4="https://www.pw.live/exams/wp-content/uploads/2024/12/curious-jr.mp4"][/video]

Perimeter of a Rectangle Formula

The perimeter of any shape is the total length of its boundary. For a rectangle, the perimeter is calculated by adding all its sides together: Perimeter of a rectangle = l+w+l+w This can be simplified to: l + l + w + w=(2 × l)+(2 × w) Or, using the following formula:

𝑃 = 2 × (𝐿 +𝑊),

Here,

𝑃 is the perimeter of a rectangle
L is the length of a rectangle, and
W is the width of a rectangle

The perimeter is a linear measure, so its units depend on the units used for length and width, such as meters, centimeters, inches, or feet. For example, a rectangle with a length of 10 meters and a width of 5 meters has a perimeter of 2 × (10+5) = 30 meters.

Composite Numbers

Perimeter of a Rectangle Real-Life Applications

Here are a few real-life applications of calculating the perimeter of a rectangle:

To measure the length of barbed wire required to create a fence around a rectangular plot of land.
To draw a border with limestone around a rectangular ground and determine how much limestone would be required to mark the ground’s total periphery.
To calculate the length of ribbon needed to decorate the edges of a rectangular gift box.
To determine the length of string lights required to outline the boundary of a rectangular patio or garden.
To measure the total distance a runner covers when completing one lap around a rectangular track.
To figure out how much paint or tape is required to mark the boundaries of a rectangular sports court or field.

Perimeter of a Rectangle Solved Examples

Example 1: Find the perimeter of the below rectangle.

Solution: To calculate the perimeter of a rectangle, you add the lengths of all its sides. Here's how it's done: Step 1: Identify the Dimensions

Length of the rectangle: 13 units

Width of the rectangle: 3 units Step 2: Add All Sides The opposite sides of a rectangle are equal. Therefore, the rectangle has:

Two sides of 13 units each
Two sides of 3 units each

Add all the sides of a rectangle 13 + 3 + 13 + 3 = 32 units Step 3: Use the Formula (Optional) Alternatively, use the perimeter formula: Perimeter=2×(Length+Width) Substitute the values: Perimeter=2×(13+3) = 2×16 = 32 units The perimeter of the rectangle is 32 units .

Example 2: A rectangular garden has a length of 15 meters and a width of 10 meters. Find the perimeter.

Solution: The formula for the perimeter of a rectangle is: Perimeter = 2×(Length + Width) Substitute the values: Perimeter=2 × (15 +10) Perimeter = 2 × 25 = 50 meters Therefore, the perimeter of the garden is 50 meters . Example 3: A rectangular field has a length of 25 meters and a width of 20 meters. If fencing costs $5 per meter, calculate the total cost of fencing the field. Solution: First, calculate the perimeter: Perimeter=2×(Length+Width) Perimeter= 2× (25+20) = 2 × 45 Perimeter = 90 meters Now calculate the cost: Cost = Perimeter × Cost per meter Cost = 90 × 5 = 450 dollars Therefore, t he total cost of fencing is $450 .

Example 4: A rectangular playground has a perimeter of 60 meters, and its length is 20 meters. Find the width.

Solution: Use the perimeter of rectangle formula: Perimeter = 2 × (Length + Width) Substitute the known values: 60 = 2 × (20 + width) = 60 = 40 + 2 width. Divide by 2: 30 = 20 + Width Width = 30 − 20=10 meters Therefore, the width of the playground is 10 meters . Example 5: A rectangular area has a length of 12 meters and a width of 8 meters. If each toy block is 1 meter long, how many blocks are needed to form the boundary? Solution: Calculate the perimeter: Perimeter=2×(Length+Width Perimeter =2×(12+8) Perimeter = 2 × 20 = 40 meters Since each block is 1 meter long: Number of blocks = Perimeter ÷ Length of each block Number of blocks = 40 ÷ 1 = 40 Therefore, Ryan needs 40 blocks to create the boundary. Example 6: The diagonal of a rectangle measures 15 units, and its length is 9 units. Determine the perimeter of the rectangle. Solution: Given:

Diagonal = 15 units
Length = 9 units

To find the perimeter of the rectangle, follow these steps:

Step 1: Calculate the square of the diagonal and length.

Step 2: Subtract the square of the length from the square of the diagonal.

Step 3: Take the square root of the result.

√144 = 12

Step 4: Use the results to find the perimeter.

The perimeter of the rectangle is 42 units .

Related Articles
Area of Rectangle	Isosceles Triangle
What is an Abacus?	Math Puzzles
Multiplication Worksheets	Multiplication Sums

Perimeter of Rectangle FAQs

Is the Area and Perimeter of a Rectangle the Same?

No, the area and perimeter of a rectangle are not the same. The area refers to the total space enclosed within the rectangle and is expressed in square units such as square meters (m²) or square centimeters (cm²). It is calculated using the formula Area= Length ×Width. On the other hand, the perimeter is the total length of the rectangle’s boundary and is measured in linear units such as meters (m) or centimeters (cm). It is calculated using the formula: 2×(Length+Width)

How can you find the length of a rectangle with the given width and perimeter?

To find the length, use the formula: Length = Perimeter/ 2−Width Subtract the width from half the perimeter to calculate the length.

Can a rectangle have the same area and perimeter?

Yes, this happens when the rectangle's dimensions satisfy specific conditions, like a rectangle with length 4 and width.

Can you find the space covered by a rectangle using the perimeter formula?

No, the perimeter only measures the boundary length. To find the space covered, use the area formula: Area = Length×Width. The area is expressed in square units.

What happens to the perimeter if both length and width are doubled?

The perimeter also doubles because it depends linearly on the dimensions.

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Perimeter of Rectangle: Suppose you are helping your family build a vegetable garden in the backyard. To keep it safe from animals, you need to fence it completely.

What is a Rectangle?

Vertical Line

What is the Perimeter of a Rectangle?

Perimeter of a Rectangle Formula

𝑃 = 2 × (𝐿 +𝑊),

Here,

𝑃 is the perimeter of a rectangle
L is the length of a rectangle, and
W is the width of a rectangle

Composite Numbers

Perimeter of a Rectangle Real-Life Applications

Here are a few real-life applications of calculating the perimeter of a rectangle:

To measure the length of barbed wire required to create a fence around a rectangular plot of land.
To draw a border with limestone around a rectangular ground and determine how much limestone would be required to mark the ground’s total periphery.
To calculate the length of ribbon needed to decorate the edges of a rectangular gift box.
To determine the length of string lights required to outline the boundary of a rectangular patio or garden.
To measure the total distance a runner covers when completing one lap around a rectangular track.
To figure out how much paint or tape is required to mark the boundaries of a rectangular sports court or field.

Perimeter of a Rectangle Solved Examples

Example 1: Find the perimeter of the below rectangle.

Solution: To calculate the perimeter of a rectangle, you add the lengths of all its sides. Here's how it's done: Step 1: Identify the Dimensions

Length of the rectangle: 13 units

Width of the rectangle: 3 units Step 2: Add All Sides The opposite sides of a rectangle are equal. Therefore, the rectangle has:

Two sides of 13 units each
Two sides of 3 units each

Example 2: A rectangular garden has a length of 15 meters and a width of 10 meters. Find the perimeter.

Example 4: A rectangular playground has a perimeter of 60 meters, and its length is 20 meters. Find the width.

Diagonal = 15 units
Length = 9 units

To find the perimeter of the rectangle, follow these steps:

Step 1: Calculate the square of the diagonal and length.

Step 2: Subtract the square of the length from the square of the diagonal.

Step 3: Take the square root of the result.

√144 = 12

Step 4: Use the results to find the perimeter.

The perimeter of the rectangle is 42 units .

Related Articles
Area of Rectangle	Isosceles Triangle
What is an Abacus?	Math Puzzles
Multiplication Worksheets	Multiplication Sums