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:
- 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.
- The perimeter of a rectangle is twice the sum of its length and width. This property can be expressed as:
Perimeter = 2(l + w)
- 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
