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Perimeter of a Rectangle – Definition with Solved Examples

perimeter of a rectangle

A rectangle is a quadrilateral (four-sided polygon) with opposite sides equal and parallel to one another and all four vertices 90 degrees. Since the opposite sides of a rectangle are equal and parallel, it is also known as a parallelogram. A rectangle is defined by its length and breadth, which are distinct sizes, making it different from a square.

The following are the characteristics of a rectangle:

  • It has four sides and four vertices
  • The opposite two pairs of sides are parallel and equal.
  • Each vertex is at a 90-degree angle.
  • Diagonals are bisectors of each other.
  • It’s a right-angled parallelogram.
  • Sum of all interior angles equal to 360 degrees

How to find the perimeter of a rectangle?

The perimeter of a rectangle is defined as the total distance covered by the outer boundary of the rectangle. It is measured in unit length. The formula of the perimeter is given by:

Perimeter, P = 2 (Length + Width) 

The perimeter of the rectangle could be considered one of the important formulae of the rectangle. It is the total distance covered by the rectangle around its outside. Perimeter gives the length of the figure. 

The perimeter of a rectangle is equal to its sides added together. The entire distance around the sides of any object is calculated using perimeter formulas. Since the opposite sides of a rectangle are equal, the perimeter is equal to twice the length plus twice the rectangle’s width, denoted by the letter “P.”

The perimeter of a rectangle, according to the definition of the perimeter, is P = 2(a+b) units

where,

“a” is the length of the rectangle

“b” is the breadth of the rectangle

The perimeter of a Rectangle (Derivation)

Since the perimeter is equal to the sum of the polygon’s sides. As a result, the perimeter (P) of a rectangle is:-

P = all four sides added up

P = a + b + a + b   (Opposite sides of rectangle are equal)

P = 2(a + b)

where,

“a” is the length of the rectangle

“b” is the breadth of the rectangle

Therefore,

Perimeter of a rectangle = 2(Length + Width) square units

The perimeter of a Rectangle Problems

Q. Find the perimeter of a rectangle with 20 cm and 12 cm, length and breadth respectively.

  1. We know that, Perimeter of a rectangle  = 2(a + b)

where,

“a” is the length of the rectangle

“b” is the breadth of the rectangle

∴ P = 2(20+12) = 2(32) = 64 cm

Q. What is the perimeter of a rectangle 12 meters long with a 4-meter wide base?

  1. We know that, Perimeter of a rectangle  = 2(a + b)

where,

“a” is the length of the rectangle

“b” is the breadth of the rectangle

∴ P = 2(12+4) = 2(16) = 32 m

Q. What is the length of the rectangular field which has a perimeter of 120 cm and a width of 50 cm?

  1. We know that, Perimeter of a rectangle  = 2(a + b)

where,

“a” is the length of the rectangle

“b” is the breadth of the rectangle

Let P be the perimeter,

∴ P = 2(a+b) 

Or 120 = 2(a+50)

120/2 = a+50

a = 60-50

a = 10 cm

Hence, the length of the rectangular field is 10 cm. 

Q. A rectangular yard has a length of 53 m and a perimeter of 136 m. Determine its breadth.

  1. P = 136m (Perimeter of the yard)

L = 53m (Length of the yard)

Let B be the breadth of the yard.

We know that, Perimeter, P = 2(length + breadth)

Therefore,

136= 2(53 + breadth)

53 + B = 68

W = 68 – 53 = 15 m

Hence, the breadth of the yard is 15m

Q. A garden has a length of 120 inches and a width of 85 inches. How much fence will be required to surround it?

  1. To determine how much fence will be required for the garden’s border, we will calculate the perimeter of the garden using the perimeter of the rectangle formula. (Since the fence is built on a garden’s border)

Given, 

Length (L) = 120 inches 

Breadth (B) = 85 inches

A rectangle’s perimeter equals 2(l + w). When we substitute the length and width numbers in this calculation, we obtain Perimeter = 2(l + w) = 2(120 + 85) = 2×205 = 410 inches.

We’ll need 410 inches of lace to wrap around the bedsheet.

Q. A chocolate bar is made up of equal-sized squares with 1-inch sides. Determine the perimeter of the rectangular chocolate bar.

  1. Each small square has one inch on all of its sides. 

Therefore,  if we count and add the sides of the squares along the length of the bar, We obtain 6 inches as the length (L). 

Squares along the width of the bar have sides that sum up to 2 inches.

As a result, the length of the bar is 6 inches, and the width is 2 inches. 

Perimeter=2(l + w) = 2 (6 + 2) = 2×8 = 16 inches

As a result, the perimeter is 16 inches.

Relation between a Rectangle and a Square

A square is a quadrilateral with all sides equal and parallel to one another and all four vertices 90 degrees. The sole difference between this and a rectangle is that adjacent sides are also equal in addition to opposite sides, resulting in a square with equal length and width.

Therefore, The method for calculating the perimeter of a rectangle differs from the formula for calculating the perimeter of a square:-

The formula for calculating the perimeter of a rectangle is

Perimeter of rectangle = 2(a + b), 

where ‘a’ denotes the length

and ‘b’ denotes the width. 

The perimeter of a square formula, on the other hand, is defined as the

The perimeter of a square = 4s, 

where ‘s’ is the side length.

A rectangle’s perimeter formula differs from that of a square. This is because only the opposite sides of a rectangle are equal. On the other hand, a square’s sides are all the same length.

As a result, we can rewrite the formula for calculating the perimeter of a rectangle into a square as follows:

Perimeter of rectangle = 2(a + b), 

where ‘a’ denotes the length

    and ‘b’ denotes the width. 

As we know, a square’s all sides are equal, a=b=s (sides of the square),

Perimeter of rectangle = 2(a + b) = 2(s + s) = 2 x 2s = 4s

A shape’s perimeter is the distance around its edges. The distance would take to walk around the shape once along its edge. A shape’s perimeter can alternatively be defined as the sum of the lengths of all its sides.

A rectangle is a four-sided polygon (quadrilateral) with opposite sides of the same length and interior angles that are all 90 degrees. Since opposite sides have the same length, we sum the lengths of two adjacent sides and multiply by 2. The perimeter of a rectangle is calculated as 2(a + b), where a and b are the rectangle’s length and breadth, respectively.

The perimeter formula for a rectangle varies from that of a square. This is because only the opposite sides of a rectangle are equal. The sides of a square, on the other hand, are all the same length.

FAQs

Q1. What is a Perimeter?

The line or border surrounding a shape is known as its perimeter. It can also be described as the length of a shape’s outline. The simplest formula for calculating the perimeter is to sum the lengths of all the sides.

Q2. What is a Rectangle’s Perimeter?

The perimeter of a rectangle is defined as the entire distance covered by the rectangle’s outside boundary. It is measured in terms of unit length. The perimeter formula is as follows:

Perimeter of a Rectangle = 2 (Length + Width) 

A rectangle’s perimeter is equal to the sum of its sides. Perimeter formulae are used to compute the total distance around the sides of any object. Since the opposite sides of a rectangle are equal, the perimeter equals twice the rectangle’s length plus twice its breadth.

Q3. What are the distinguishing characteristics of a rectangle?

A rectangle has four sides and four vertices, of which Opposite two sides are parallel and equal, and each vertex forms a 90-degree angle. The diagonals of a rectangle are bisectors to each other. We can also call a rectangle a right-angled parallelogram.

Q4. What is the sum of a rectangle’s all internal angles?

The sum of a rectangle’s all internal angles equals 360 degrees.

Q5. What’s the difference between a Rectangle and a Square? How does it affect their Perimeter formulas?

A square is defined as a four-sided polygon (quadrilateral) with all sides equal and parallel to one another and all four vertices that are 90 degrees. The only difference here from a rectangle is that adjacent sides are also equal in addition to being opposite; hence, the length and breadth of a square are equal.

The perimeter formula for a rectangle varies from that of a square. This is because only the opposite sides of a rectangle are equal. The sides of a square, on the other hand, are all the same length.

As a result, we can change the formula for a rectangle’s perimeter into a square as follows:

Rectangle perimeter = 2(a + b), where ‘a’ represents length and ‘b’ represents breadth.

Now the sides of a square are all equal, a=b=s (sides of the square),

Therefore, Rectangle perimeter = 2(a + b) = 2(s + s) = 2 x 2s = 4s

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