What is a Rectangle?
A rectangle is a quadrilateral in which the opposite sides are parallel and equal, and each angle of a rectangle is equal to 90\(^{\circ}\). One of the properties of a rectangle is that the length is the longer side, and the width is the shorter side.
Rectangular Shaped Objects around Us
We come across various examples of rectangular shapes in our daily life. Rectangles are the most commonly seen shapes in daily life. A few of the objects we encounter are white boards, postcards, doors, cell phones, study tables, and many others.
What is the Perimeter of a Rectangle?
The perimeter of a rectangle is the sum of the length of its all sides. As seen earlier, a rectangle has four sides, with the opposite sides equal.
Thus, the perimeter of the rectangle is the sum of the length of all four sides. It is a linear measure so the perimeter is expressed in units such as meters(m), centimeters(cm), inches(in) or feet(ft).
Formula of Perimeter of Rectangle
The perimeter of a geometric shape is defined as the total distance covered by its boundaries. For example in any polygon, the perimeter formula is the sum of the length of its sides. Thus, the perimeter of a rectangle is twice the sum of its length and width, and is denoted by the letter ‘p’.
Suppose a rectangle having length ‘l’ and width ‘w’.
Perimeter of rectangle = sum of all its sides
So, the perimeter of the rectangle = length + width + length + width
PERIMETER OF RECTANGLE = 2( l + w ) units
where,
l = length of the rectangle
w = width of the rectangle
Application of the Perimeter of a Rectangle
The various examples in our everyday life which is very common and based on perimeter of rectangle, some of them are listed below;
- The length of a rectangular field or garden is also determined by the formula of the perimeter of the rectangle.
- If we construct a house, then we find the length of its boundary with the help of the perimeter formula.
- If we hang an electric board on a wall then we determine the length by the perimeter formula.
- The formula of perimeter is used in various ways to create projects, crafts, and decorate any rectangular shape.
Solved Examples
Example 1: The length of a rectangle is 9 cm and the width is 12 cm. Find the perimeter of the rectangle.
Solution:
As stated in the question,
length(l) = 9 cm
width(w) = 12 cm
Perimeter of rectangle = 2( l + w ) [Use formula]
= 2( 9 + 12 ) [Substitute the value of l and w]
= 2(21) [Apply PEMDAS rule]
P = 42 cm [Multiply]
So, the perimeter of the rectangle is 42 centimeters.
Example 2: The width of the rectangular garden is 15 ft and its perimeter is 120 ft. Find its length.
Solution:
As stated in the question,
Perimeter of the rectangular garden, P = 120 ft
width of the rectangular garden, w = 15 ft
Let l be the length of the garden.
Perimeter, P = 2( length + width ) [Use formula]
120 = 2( 15 + l ) [Substitute the value]
60 = 15 + l [Divide both sides by 2]
60 \(-\) 15 = l [Subtract both sides by 15]
l = 45 ft [Subtract]
So, the length of the garden is 45 feet.
Example 3: The length of the rectangular sign board is 20 feet and its perimeter is 130 feet. Find its width.
Solution:
As stated in the question,
Perimeter of the rectangular board, P = 130 feet
length of the rectangular garden, l = 20 feet
Let w be the width of the board.
Perimeter, P = 2( length + width ) [Use formula]
130 = 2( 20 + w ) [Substitute the value]
65 = 20 + w [Divide both sides by 2]
65 \(-\) 20 = w [Subtract both sides by 20]
W = 45 ft [Subtract]
So, the width of the sign board is 45 feet.
The sum of the length of all four sides of a rectangle is known as the perimeter of the rectangle.
Perimeter of rectangle = 2( l + w ).
Where ‘l’ is the length of the rectangle and ‘w’ is the width of the rectangle.
Perimeter is the sum of the side lengths of the rectangle. Hence, it is always measured in units such meters(m), centimeters(cm), inches(in), feet(ft) and other related units of length.