Question

Find the general rule for the perimeter of a rectangle. Use variables $'l'$ and $'b'$ for length and breadth of the rectangle respectively.

Answer 1

Hint:The perimeter basically gives the length of any shape. In the case of a rectangle there are two lengths and two breadths, therefore perimeter will be the sum of all the sides.

Complete step-by-step answer:
We are given the variables $'l'$ and $'b'$ for length and breadth of the rectangle respectively.
We have to find the general rule or formula for the perimeter of the given rectangle.
First, we draw the shape of the rectangle in order to understand the perimeter in detail.

Here, we have a rectangle ABCD.
We know that the opposites of the rectangles are equal.
Therefore, $AB = CD = l$ and $BC = AD = b$ here, AB and CD are the lengths of the rectangle and BC and CD are the breadths of the rectangle.
We know that the perimeter of any shape is nothing but the length of the whole shape.
In the rectangle, there are two equal lengths and two equal breadths as seen in the figure.
To evaluate the total length of the rectangle, we have to add the measurement of all the sides.
Let the perimeter of the rectangle is P.
Therefore, the perimeter is defined as:
$P = AB + BC + CD + DA$
Substitute all the values and evaluate the perimeter of the rectangle.
$ \Rightarrow P = l + b + l + b$
Combine the like terms and make the general rule for the perimeter of the rectangle.
$
  P = l + l + b + b \\
   \Rightarrow P = 2l + 2b \\
   \Rightarrow P = 2(l + b) \\
 $
Hence, the general rule or formula for the perimeter of the rectangle is $2(l + b)$.

Note:We have evaluated the perimeter of the rectangle which is $2(l + b)$. We can say that the perimeter of the rectangle is twice the sum of the length and the breadth of the rectangle.