In mathematics, you study different types of plane figures generally known as 2D shapes. Perimeter is one of the basic and important concepts in measurement. Perimeter basically gives the length of the figure. If you start from one vertex of a figure and move along all the edges (sides) one by one covering all and reaching back to the vertex you started with, the distance (length) covered is the perimeter of a figure.
Let’s learn what is the perimeter of a rectangle and how it is calculated.
Rectangle – A 2D Plane Figure
A rectangle is a 2D shape, whose opposite sides are equal and parallel. The measure of all four angles of a rectangle is equal and it is $90^{\circ}$.
What is the Perimeter of a Rectangle?
The perimeter of a rectangle is the total distance covered by its boundaries or sides. Since there are four sides of a rectangle, thus, the perimeter of the rectangle will be the sum of all four sides. Since the perimeter is a linear measure, therefore, the unit of the perimeter of a rectangle will be in metre, centimetre, inch, feet, etc.
Usage of Perimeter of a Rectangle
The perimeter of a rectangle makes things easier and helps us in calculating distances and lengths in our day-to-day lives.
For example,
- If you need to decorate the border of your rectangular notebook, you can easily calculate how much ribbon you would need by finding the perimeter.
- If you need to put a fence around your garden, the perimeter of the garden will give you the exact length of wire you would need.
- For the construction plan of the house, we need to set a boundary using concrete which is possible by the perimeter formula.
Perimeter of a Rectangle Formula
The perimeter of a rectangle is defined as the sum of all the sides of a rectangle. The formula for the perimeter of any polygon is the sum of all its edges (sides). In the case of a rectangle, the opposite sides of a rectangle are equal and so, if the two adjacent sides are $l$ and $w$, the perimeter of a rectangle is given by the formula $P = 2\left(l + w \right)$.
Derivation of Perimeter of Rectangle Formula
Consider a rectangle ABCD, whose length is $l$ and the width is $w$.
From the figure, you can see lengths are $AB = CD = l$ and widths are $BC = DA = w$.
The total length of the boundary of a rectangle = $AB + BC + CD + DA = l + w + l + w = 2l + 2w = 2\left(l + w \right)$.
How to Find the Perimeter of a Rectangle?
You can calculate the perimeter of a rectangle using the following three simple steps.
Step 1: Note down the length and width of a rectangle
Step 2: Convert the length and width to the same units, if units of length and width are not the same
Step 3: Substitute the values of length and width of a rectangle in the formula.
Step 4: Simplify the expression in the formula to get the perimeter.
Examples
Ex 1: Find the perimeter of a rectangle whose length is $12 cm$ and width is $7 cm$.
Length of rectangle $l = 12 cm$
Width of rectangle $w = 7 cm$
Perimeter of a rectangle $P = 2\left(l + w\right)$
Substitute the values of $l$ and $w$ in the formula.
$P = 2\left(12 + 7\right) = 2 \times 19 = 38 cm$.
Therefore, the perimeter of a rectangle of length and width $12 cm$ and $7 cm$ is $38 cm$.
Note:
- The unit of the perimeter is $cm$.
- $cm^{2}$, $m^{2}$, $mm^{2}$, etc. are units of area
Ex 2: Find the perimeter of a rectangle whose length is $2 m$ and width is $80 cm$.
Length of rectangle $l = 2 m$
Width of rectangle $w = 80 cm$
Observe that the length and width do not have the same unit. So, you’ve to convert either $m$ to $cm$ or $cm$ to $m$.
Let’s convert the width is $m$.
Width $w = 80 cm = \frac {80}{100} = 0.80 m$.
Perimeter of a rectangle $P = 2\left(l + w\right)$
Substitute the values of $l$ and $w$ in the formula.
$P = 2\left(2 + 0.80\right) = 2 \times 2.80 = 5.60 m$.
Therefore, the perimeter of a rectangle of length and width $2 m$ and $80 cm$ is $5.60 m$.
You can also find the perimeter by converting the unit of length into centimetre.
Length = $2 m = 2 \times 100 = 200 cm$.
Perimeter of a rectangle $P = 2\left(l + w\right)$
Substitute the values of $l$ and $w$ in the formula.
$P = 2\left(200 + 80\right) = 2 \times 280 = 560 cm$.
Therefore, the perimeter of a rectangle of length and width $2 m$ and $80 cm$ is $560 cm$.
Note: The lengths $5.60 m$ and $560 cm$ are the same. $5.60 m = 5.60 \times 100 = 560 cm$.
Ex 3: Find the width of a rectangle whose length is $28 cm$ and perimeter is $80 cm$.
Length of rectangle $l = 28 cm$
Perimeter of rectangle $P = 80 cm$
Perimeter of rectangle $P = 2\left(l + w\right)$
$=>80 = 2\left(28 + w\right) => \frac {80}{2} = 28 + w => 40 = 28 + w => w = 40 – 28 => w = 12 cm$.
Therefore, the width of a rectangle whose length is $28 cm$ and perimeter is $80 cm$ is $12 cm$.
Alternatively,
Perimeter of rectangle $P = 2\left(l + w\right)$
$=> w = \frac {P}{2} – l => w = \frac {80}{2} – 28 = 40 – 28 = 12 cm$.
Ex 4: The length of a bedsheet is $120$ inches and the width is $85$ inches. How much lace will be needed to put around its border?
Length of rectangular bedsheet = $120 in$
Width of rectangular bedsheet = $85 in$
Perimeter of rectangle $P = 2\left(l + w\right)$
$=> P = 2 \left(120 + 85 \right) = 2 \times 205 = 410 in$
The length of lace needed to put around a bedsheet of length $120$ inches and the width $85$ inches is $410$ inches.
Ex 5: Ravi is running around a rectangular park of length $14 m$ and width $8 m$. Find the distance covered by him in
- $1$ round
- $5$ rounds
Length of rectangular park $l = 14 m$
Width of rectangular park $w = 8 m$
The distance covered around the rectangular park in one round is equal to the perimeter of a rectangle.
Perimeter of rectangle $P = 2\left(l + w\right)$
$=> P = 2\left(14 + 8\right) = 2 \times 22 = 44 m$
Distance covered by Ravi in one round = $44 m$.
And distance covered by Ravi in $5$ rounds is $44 \times 5 = 220 m$.
Ex 6: Sonu wants to fence his rectangular garden of dimensions $5 m$ by $2.2 m$. If the cost of the fence is ₹$150$ per metre, find the total cost of fencing.
Length of rectangular garden $l = 5 m$
Width of rectangular garden $w = 2.2 m$
Perimeter of rectangle $P = 2\left(l + w\right)$
$=>P = 2 \left(5 + 2.2\right) = 2 \times 7.2 = 14.4 m$
Rate of fence per metre = ₹$150$ per metre
Therefore, total cost of fencing = $14.4 \times 150 =$₹ $2160.00$
Ex 7: Your favorite chocolate bar is made up of equal-sized squares with each side measuring $1$ inch. Calculate the perimeter of the rectangular choco bar.
The number of squares along the length of the chocolate bar is $6$.
Therefore, the length of rectangular chocolate bar = $1 \times 6 = 6 in$
The number of squares along the length of the chocolate bar is $2$.
Therefore, the length of rectangular chocolate bar = $1 \times 2 = 2 in$
Perimeter of rectangle $P = 2\left(l + w\right)$
$=> P = 2\left(6 + 2 \right) = 2 \times 8 = 16 in$.
The perimeter of a chocolate bar is $16 in$.
Perimeter of Rectangle Formula vs Perimeter of Square Formula
The perimeter of a rectangle formula is different from the formula for the perimeter of a square.
- The perimeter of a rectangle formula is expressed as Perimeter of rectangle = $2\left(l + w \right)$, where $l$ is the length and $w$ is the width. However, the perimeter of a square formula is expressed as, the perimeter of a square = $4 \times s$, where $s$ is the side length.
- The perimeter of a rectangle formula is different from the perimeter of a square because only the opposite sides of a rectangle are equal. However, in the case of a square, all the sides are of equal length.
Conclusion
The perimeter of any 2D plane shape is the sum of all its sides. As the opposite sides of a rectangle are equal, its perimeter is given the formula $P = 2\left(l + w\right)$, where $l$ and $w$ are the lengths of two adjacent sides commonly known as length and width.
Practice Problems
- Find the perimeter of a rectangle whose length and width are
- length = $7 cm$ and width = $4 cm$
- length = $15 in$ and width = $11 in$
- Find the length of a rectangle whose perimeter and width are
- perimeter = $42 ft$ and width = $8 ft$
- perimeter = $68 in$ and width = $12 ft$
- Find the width of a rectangle whose perimeter and length are
- perimeter = $98 cm$ and width = $20 cm$
- perimeter = $54 in$ and width = $15 in$
- Shweta wants to fence her rectangular garden measuring $7 m$ by $3.5 m$. Find the length of fencing material required. Also, find the total cost of the fencing material at the rate of ₹$140$ per metre.
- A runner makes $15$ complete rounds of a rectangular ground of length $200 m$ and width $150 m$. Find the distance in kilometres covered by the runner.
Recommended Reading
- What is Length? (With Definition, Unit & Conversion)
- Weight – Definition, Unit & Conversion
- What is Capacity (Definition, Units & Examples)
- What is Time? (With Definition, Facts & Examples)
- What is Temperature? (With Definition & Units)
- Reading A Calendar
- Perimeter of Square – Definition, Formula & Examples
FAQs
What is the perimeter of a rectangle in math?
The perimeter of a rectangle in math is defined as the total length or distance around the boundary of a rectangle. The perimeter of a rectangle is measured in linear units like meters, feet, inches, yards, and so on.
What is a formula for the perimeter of a rectangle?
The perimeter of a rectangle is the total length around the boundary of a rectangular shape. For a rectangle of length $l$ and width $w$, the perimeter is given by $P = 2\left(l + w \right)$.
How to calculate the perimeter of a square?
The perimeter of a rectangle of length $l$ and width $w$ can be calculated by using the formula $P = 2\left(l + w \right)$.
Can we find the length of a rectangle, if its perimeter and width are known?
Yes, we can find the length of a rectangle, if its perimeter and width are known. The formula used is $l = \frac {P}{2} – w$, where $P$, $l$ and $w$ are the perimeter, length and width of a rectangle.
Can we find the width of a rectangle, if its perimeter and length are known?
Yes, we can find the width of a rectangle, if its perimeter and length are known. The formula used is $w = \frac {P}{2} – l$, where $P$, $l$ and $w$ are the perimeter, length and width of a rectangle.
