1. Rectangle
A rectangle is a quadrilateral with four right angles. It has two pairs of opposite sides that are equal. The longer side is usually called the length (l) and the shorter side is called the breadth (b).
Because opposite sides repeat in pairs, the boundary of a rectangle follows the pattern: length → breadth → length → breadth.
1.1. Definition of Perimeter
The perimeter of any 2D shape means the total distance around its boundary. For a rectangle, we add the lengths of all four sides.
Since a rectangle has two lengths and two breadths, its perimeter is obtained by adding these four values.
2. Perimeter Formula
To find the perimeter of a rectangle, we add length and breadth twice. This gives us the standard formula:
\( P = 2(l + b) \)
2.1. Working of the Formula
The boundary of a rectangle is made of:
- two sides of length \(l\)
- two sides of breadth \(b\)
So, total perimeter becomes:
\( P = l + b + l + b = 2l + 2b = 2(l + b) \)
This is why we multiply the sum of length and breadth by 2.
3. Examples
Let’s understand the formula better using simple examples.
3.1. Example 1
A rectangle has length \(l = 12\text{ cm}\) and breadth \(b = 5\text{ cm}\). Its perimeter is:
\( P = 2(l + b) = 2(12 + 5) = 2 \times 17 = 34\text{ cm} \)
3.2. Example 2
A rectangular garden has length \(l = 20\text{ m}\) and breadth \(b = 10\text{ m}\). The boundary length is:
\( P = 2(l + b) = 2(20 + 10) = 2 \times 30 = 60\text{ m} \)