Maths

# Write The Perimeter Of The Rectangle As A Simplified Expression

Perimeter refers to the distance around a geometric figure or the length of the boundary that encloses it. The perimeter of a rectangle is the sum of the lengths of all four sides. When given the length and width of a rectangle, we can write the perimeter as a simplified expression. In this article, we will explore the concept of perimeter of a rectangle and learn how to write it as a simplified expression (How write the perimeter of the rectangle as a simplified expression).

## Understanding the Rectangle

A rectangle is a four-sided polygon with opposite sides parallel and equal in length. It is a special case of a parallelogram where all angles are right angles. The length and width of a rectangle are its two adjacent sides. The area of a rectangle is calculated by multiplying its length and width.

## Perimeter Of A Rectangle

The perimeter of a rectangle is the total length of all its sides. It is calculated by adding the length of all four sides of a rectangle. The formula for the perimeter of a rectangle is given as follows:

Perimeter = 2(length + width)

Alternatively, the perimeter of a rectangle can be expressed as:

Perimeter = 2l + 2w

Where l is the length and w is the width of the rectangle.

## Writing The Perimeter Of A Rectangle As A Simplified Expression

To write the perimeter of a rectangle as a simplified expression, we need to know the values of its length and width. Let us consider an example where the length of a rectangle is 7 cm and the width is 4 cm.

Using the formula for the perimeter of a rectangle, we can write the expression for its perimeter as:

Perimeter = 2(length + width)

Substituting the values of length and width, we get:

Perimeter = 2(7 + 4)

Simplifying the expression within the parentheses, we get:

Perimeter = 2(11)

Multiplying 2 by 11, we get:

Perimeter = 22

Therefore, the perimeter of the rectangle with length 7 cm and width 4 cm is 22 cm.

## Examples Of How To Write The Perimeter Of The Rectangle As A Simplified Expression

Let us consider a few more examples to understand how to write the perimeter of a rectangle as a simplified expression.

• Example 1: Given the length of a rectangle is 6 cm and width is 5 cm, find its perimeter.

Perimeter = 2(length + width)

Substituting the values of length and width, we get:

Perimeter = 2(6 + 5)

Simplifying the expression within the parentheses, we get:

Perimeter = 2(11)

Multiplying 2 by 11, we get:

Perimeter = 22

Therefore, the perimeter of the rectangle with length 6 cm and width 5 cm is 22 cm.

• Example 2: Given the length of a rectangle is 10 cm and its perimeter is 36 cm, find its width.

Let us assume that the width of the rectangle is w.

Perimeter = 2(length + width)

Substituting the values of length and width, we get:

36 = 2(10 + w)

Simplifying the expression within the parentheses, we get:

36 = 20 + 2w

Subtracting 20 from both sides of the equation, we get:

16 = 2w

Dividing both sides of the equation by 2, we get:

w = 8

Therefore, the width of the rectangle is 8 cm.

• Example 3: Given the perimeter of a rectangle is 24 cm and its width is 3 cm, find its length.

Let us assume that the length of the rectangle is l.

Perimeter = 2(length + width)

Substituting the values of perimeter and width, we get:

24 =2(l + 3)

Simplifying the expression within the parentheses, we get:

24 = 2l + 6

Subtracting 6 from both sides of the equation, we get:

18 = 2l

Dividing both sides of the equation by 2, we get:

l = 9

Therefore, the length of the rectangle is 9 cm.

Properties of the Perimeter of a Rectangle

The perimeter of a rectangle has a few properties that are worth noting:

1. If the length and width of a rectangle are equal, it becomes a square. In this case, the perimeter of the square is given by:

Perimeter = 4s

Where s is the length of the side of the square.

1. The perimeter of a rectangle is twice the sum of its length and width. This property can be expressed as:

Perimeter = 2(l + w)

1. If the length of a rectangle is increased by a certain factor, while the width is decreased by the same factor, the perimeter remains constant. This property is known as the constant perimeter property.

• Example 4: Given the length of a rectangle is 12 m and its width is 6 m, find its perimeter.

Perimeter = 2(length + width)

Substituting the values of length and width, we get:

Perimeter = 2(12 + 6)

Simplifying the expression within the parentheses, we get:

Perimeter = 2(18)

Multiplying 2 by 18, we get:

Perimeter = 36

Therefore, the perimeter of the rectangle with length 12 m and width 6 m is 36 m.

Example 5: Given the perimeter of a rectangle is 28 cm and its length is 7 cm, find its width.

Let us assume that the width of the rectangle is w.

Perimeter = 2(length + width)

Substituting the values of perimeter and length, we get:

28 = 2(7 + w)

Simplifying the expression within the parentheses, we get:

28 = 14 + 2w

Subtracting 14 from both sides of the equation, we get:

14 = 2w

Dividing both sides of the equation by 2, we get:

w = 7

Therefore, the width of the rectangle is 7 cm.

Example 6: Given the width of a rectangle is 8 cm and its perimeter is 48 cm, find its length.

Let us assume that the length of the rectangle is l.

Perimeter = 2(length + width)

Substituting the values of perimeter and width, we get:

48 = 2(l + 8)

Simplifying the expression within the parentheses, we get:

48 = 2l + 16

Subtracting 16 from both sides of the equation, we get:

32 = 2l

Dividing both sides of the equation by 2, we get:

l = 16

Therefore, the length of the rectangle is 16 cm.

Example 7: Given the perimeter of a rectangle is 60 m and its width is 10 m, find its length.

Let us assume that the length of the rectangle is l.

Perimeter = 2(length + width)

Substituting the values of perimeter and width, we get:

60 = 2(l + 10)

Simplifying the expression within the parentheses, we get:

60 = 2l + 20

Subtracting 20 from both sides of the equation, we get:

40 = 2l

Dividing both sides of the equation by 2, we get:

l = 20

Therefore, the length of the rectangle is 20 m.

### Conclusion

The perimeter of a rectangle is an important concept in geometry. It is the total length of all the sides of a rectangle. The formula for the perimeter of a rectangle is given by adding the length of all four sides. To write the perimeter of a rectangle as a simplified expression, we need to know the values of its length and width. We can use the formula 2(l + w) to calculate the perimeter of a rectangle. The properties of the perimeter of a rectangle include the fact that it is twice the sum of its length and width and the constant perimeter property.

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