Perimeter of Rectangle

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What is Perimeter?

In simple words, the perimeter can be defined as the boundary or path that surrounds a two-dimensional shape. Although in this content we will focus more on the perimeter of the rectangle, you can also determine the perimeter for other figures as well.


What is a Rectangle?

As per Euclidean plane geometry, a rectangle can be defined as a quadrilateral having four sides. The term ‘rectangle’ is derived from the Latin word rectangulus, which is a mix of angulus (angle) and rectus (proper and right).


Properties of a Rectangle

The opposite sides of a rectangular shape are always identical or same.

If the angles of a rectangle are measured, you will find that the same measures 90 degrees each.

You can take a look at an example mentioned below:


(image will be uploaded soon)


How to Find the Perimeter of a Rectangle?

To determine the perimeter of the rectangle, you need to carry out a sum of all the sides. For instance, considering the above mentioned figure, it can be written as 5 + 3 + 5 + 3 = 16 units.

Note: Do not forget to write the unit, each time you solve a perimeter problem.

However, as opposite sides of a rectangle are equal, the above perimeter of rectangle formula in maths can be written as:

2 ( 5 + 3 ) = 16 units.

In other words: perimeter formula of rectangle formula: 2 x (addition of adjacent sides).

Besides rectangle, here we have provided a list of perimeter formulas for other shapes:


Perimeter Formulas

Shape

Formula

Square

a x b

Triangle (equilateral)

3 x a

Triangle (scalene)

a + b + c

Quadrilateral

a + b + c + d

Pentagon

5 x a

Hexagon

6 x a

Octagon

8 x a


Next, let’s proceed to some simple examples of finding the perimeter of a rectangle.

Problem 1. What will be the perimeter of the rectangle whose length and breadth are 12 and 7 cm, respectively?

Solution. Substituting the values in the perimeter of rectangle equation we get:

2 x (l + b) cm

= 2 x (12 + 7) cm

= 38 cm


Problem 2. If the area of a rectangle is 96 cm2, find the perimeter, provided the width of the rectangle is 4 cm less than the length.

Solution. Area of the rectangle is (l x b) which is 96 cm2 for this sum. It is said that the width of the rectangle is 4 cm less than the length, which means if the length is considered as x, then the width will be x – 4.

So, substituting the values in the area equation we get:

x (x-4) = 96

x2 – 4x – 96 = 0

x2 + 8x – 12x – 96 = 0

x(x + 8) – 12(x + 8) = 0

So, (x-12) = 0 and (x + 8) = 0

We will not consider the negative value, hence length = x = 12 cm and width = 8 cm. Now, after putting the values in the formula to find perimeter of rectangle, we get:

2 (l + b) = 2 (12 + 8) = 40 cm2.


Problem 3. Look at the following figure and find out the following:

  1. Perimeter of large rectangle.

  2. Perimeter of small rectangle.

(image will be uploaded soon)

Solution. (a) perimeter of large rectangle:

2 (l + b) = 2(6 + 8) units = 28 units

(b) Perimeter of small rectangle:

First find the length and width of the smaller rectangle.

Length of rectangle = 8 – (1 + 3) = 4 units

Width of rectangle = 6 – (2 + 2) = 2 units

Hence, 2 x (l + b) = 2 x (4 + 2) = 12 units.


Do It Yourself

  1. A room of rectangular shape has a perimeter of 150 m2. If the width of the room is 10m, what will be the length?

(a) 25m (b) 55m (c) 15m (d) 50m

  1. A rectangular piece of wire is given a shape of a square, and the length and breadth of the same are 40 cm and 20 cm. Find out the side of the square.

By going through the above discussion, you must have understood how to find the perimeter of the rectangle and related concepts. To know the perimeter formula for other shapes as well, please download the Vedantu app today!

FAQ (Frequently Asked Questions)

1. What are the Applications of the Perimeter in Real Life?

Ans. The path that surrounds or encompasses a two-dimensional place is known as the perimeter. In other words, it can also be explained as the dimension of the outline of a given space. There are various applications of the perimeter in real life. For instance, when you put up lights during Diwali or Christmas around your house or when you fence a field. Some other examples include a string or ribbon needed to cover a mat or piece of cloth or amount of track required to fit around a football stadium.

2. How to Find the Perimeter of a Triangle?

Ans. As you all know, triangles have three sides, and they may or may not be equal. For an equilateral triangle (a triangle having all sides equal), the process to find a perimeter is very easy and straightforward. Just use the formula 3 xs (sides of an equilateral triangle). Next, for an isosceles triangle, the equation 2s + b is used. Here, b is the triangle’s base length, and s is the dimension of two congruent sides. Furthermore, in case of a scalene triangle whose all sides are unequal, we just add up all the sides: p = s1 + s2 + s3.

3. What is the Perception of Area and Perimeter?

Ans. In Mathematics as well as in real life, area and perimeter play a significant role in measuring or evaluating shapes and figures, and people get easily confused between the two. However, a common-place observation states that reduction or enlargement of the figure is the reason behind maximisation of area and perimeter of a rectangle both. For example, if you sketch a figure of land on a 1/10,000 map, you can quickly find the perimeter by multiplying it with 10,000. On the other hand, the actual area is 10,000 square times greater than the value on the map. Also, note that no relation exists between the area and perimeter of a regular shape or pattern.