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A quadrilateral whose opposite sides are equal with four equal sides is called a rectangle. The perimeter of a rectangle is the sum of the lengths of all its sides. In other words, it is the total distance covered by a rectangular object along the border of a plot. In mathematics, we use meter (m), centimeter (cm), inch (in), feet (ft), yards etc. as the unit of measurement to calculate the perimeter of a rectangle.
Picture frames and cement bricks are some examples of rectangles. The perimeter for any figure is defined as the length of its boundary. In this article, we will learn more about the calculations, applications of perimeter and its relation with the area of a rectangle in mathematics.
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What is Perimeter of a Rectangle?
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Perimeter of rectangle is a linear measurement. In mathematics, both 2D and 3D shapes have a defined length, width, and volume, so perimeter and area can be easily calculated. Similarly, the rectangle is a four-sided polygon with opposite sides being parallel and equal in measure. All four angles made by the four sides are 900 (right angle).
Thus, the total length of a rectangle's boundaries or sides is known as its perimeter. To calculate the perimeter, length and width dimensions must be determined. The perimeter of rectangle can also be calculated by adding all the sides of the rectangle. Similarly, for a square with all its sides and angles equal, the perimeter of the square is calculated by simply adding all four of its sides.
Perimeter of Rectangle Formula
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The formula for the perimeter of a rectangle can be determined only when the length and breadth of the rectangle are known. As we know that in a rectangle the opposite sides are equal. Thus, the perimeter of a rectangle formula can be given as twice the length and breadth of the rectangle. Mathematically, this can be represented as:
Perimeter, (P) = 2 (l + b) units
- Where, l = length of the rectangle
- b = breadth or width of the rectangle
- P is called the perimeter of rectangle
In the case of a rectangle, the opposite sides are parallel and equal. Hence, the perimeter of rectangle is equal to twice the width plus twice the length of the rectangle. It is the total distance covered along the sides of a rectangle
Perimeter of Rectangle Formula
Solved Examples of Perimeter of RectangleGiven below are examples of perimeter of rectangle. TYPE 1: Finding Perimeter When Length and Width are KnownExample: Calculate the perimeter of a rectangle with sides of length 12 cm and breadth 8 cm.
Solution: From the figure above we know, length of rectangle= a=c breadth of rectangle = b=d Using the perimeter of the rectangle formula, In this case, Perimeter = 2(a+b) Substituting values, = 2(12 + 8) = 2 (20) = 40 cm TYPE 2: Finding the Unknown Side When One Side and Perimeter are KnownExample: The perimeter of a rectangular garden is 56 m. Determine the width of the rectangular plot, if the length of the garden is 16 m.
Solution: From the figure given, length of rectangular garden = 16 m Perimeter, P= 56 m Let the unknown side length (width) = w Perimeter of a rectangle = 2 (l + b) Substituting the values, 56= 2(16+ w) Therefore, 56 = 32 +2w Rearranging we get, 56-32 = 2w 2w= 24 w= 24/2 Width of the rectangular plot = 12 m Type 3: Finding Perimeter When Area and Length of One Side is KnownExample: A rectangular sheet of paper has an area of 500 cm2 and the length of one of its sides is 20 cm. Determine the perimeter of the rectangular sheet.
Solution: Area of the rectangular sheet, A= 500 cm2 Length of the side = 20 cm Let the breadth be = b cm Area of a rectangle = length x breadth Substituting we get, 500 = 20 x b therefore, b= 500/20 = 25 cm. Perimeter is given by P= 2(l+b) Therefore P= 2 (20+25) = 2(45) =90 cm |
Derivation of Perimeter of Rectangle
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Perimeter of a rectangle is the total length around its boundary. Let us deduce the perimeter of a rectangle formula.
Rectangle with Sides l and w
From the figure above,
let the length of the rectangle be l and the breadth or width be w
Now,
The perimeter (P)= l + l + w + w ………….. (1)
We know that in a rectangle the opposite sides are equal and parallel.
Simplifying equation (1) further we get,
P= 2l + 2w
Taking the common factor out, the equation can be reduced to,
P = 2 (l+w) units
Thus,
The perimeter of a rectangle = 2( sum of the adjacent sides of the rectangle)
How to find the Perimeter of Rectangle
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Perimeter of Rectangle can be obtained in five simple steps which are as follows:
- Identify the length and breadth or width of the rectangle given in the question.
- Convert all the linear measurements given into the same units.
- Write down the perimeter of the rectangle formula.
- Substitute the known values of length and breadth of the rectangle in the formula.
- The value calculated after substitution is the perimeter of the given rectangle.
Area and Perimeter of Rectangle
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For any figure, the area is defined as the number of square units enclosed within the boundary of the figure. Perimeter is the overall length of the boundary of the figure.
Let us consider the following rectangle, length is a unit and breadth is b unit.
Rectangle with Dimensions a and b
The area enclosed within the rectangle, A = a*b square units
The perimeter of the rectangle, P = 2 (a+b) units
Therefore, we see that there is no direct relation between the area and the perimeter of the rectangle.
Applications of Perimeter of Rectangle
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The perimeter of rectangle has several real-life practical applications. Some of the applications are listed as follows:
- Perimeter of rectangle formula can be used to calculate the length of a rectangular field.
- It can also be used to calculate the fence of the garden.
- It can be used for a variety of art and craft projects.
- Some craft projects include adding colourful ribbons or ropes of rectangular cardboard.
- The perimeter of rectangle is used to determine the length of swimming races.
- It is determined when constructing a rectangular swimming pool.
- Concrete border for a house construction plan, which is feasible using the perimeter formula.
Things to Remember
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- The perimeter of rectangle is given by the formula P = 2 [l+b].
- A perimeter is the length of the boundary of any geometric figure.
- It can be easily determined by adding the length of the sides of the figure.
- It is measured in linear units like meters, centimetres, millimetres, etc.
- The perimeter for a rectangle can be calculated in 5 simple steps.
Sample Questions
Ques. What is the area and perimeter of a rectangle? (2 Marks)
Ans. In two-dimensional space, the area of a rectangle is defined as the area that the rectangle covers. The number of square units required to entirely fill a rectangle can also be defined as its area,
Area of Rectangle = (l × b)
The perimeter of a rectangle is the total distance around the rectangle's outside. In simple terms, the perimeter of a rectangle is its whole boundary,
Perimeter of a Rectangle = 2 (l + b).
Ques. Calculate the perimeter of a rectangular swimming pool of length of 7.5m and breadth of 5m? (2 Marks)
Ans. We know that,
Perimeter of Rectangle = 2[l+b]
Therefore,
Perimeter of Rectangular swimming pool = 2[7.5+5]
Perimeter = 25m
Ques. Calculate the length of the photo frame required for a picture of size 30 cm x 50 cm? (2 Marks)
Ans. We know that,
Perimeter of Rectangle = 2[l+b]
Perimeter of Rectangular picture = 2[30+50]
Length of photo frame required = 160cm
Ques. Calculate the perimeter of a rectangular garden of length of 20m and breadth of 10m? (1 Mark)
Ans. We know that,
Perimeter of Rectangle = 2[l+b]
Perimeter of Rectangular garden = 2[20+10]
Perimeter = 60m
Ques. Calculate the amount required for fencing the perimeter of a rectangular garden of length of 8m and breadth of 6m at the rate of Rs. 10 per meter? (2 Marks)
Ans. We know that,
Perimeter of Rectangle = 2[l+b]
Perimeter of Rectangular garden = 2[8+6]
Perimeter = 28m
Rate of fencing = Rs.10/m
Rate of fencing 28 m = 28 x10 = Rs.280
Ques. How do you calculate the perimeter of a rectangle? (1 Mark)
Ans. Add all the sides of a rectangle to get the perimeter. A rectangle has four sides, the total of which determines its perimeter.
Ques. What is the formula for calculating the perimeter of a rectangle? (1 Mark)
Ans. P = length + breadth + length + breadth is the formula for calculating the perimeter of a rectangle.
Since the opposite sides are equal in length,
P = 2(length + breadth)
Ques. What is the difference between a rectangle and a parallelogram? (2 Marks)
Ans. The main difference between a rectangle and a parallelogram is that opposite sides in a parallelogram are equal and adjacent sides are perpendicular to each other.
- However, in a rectangle, opposite sides are parallel and equal and adjacent sides are perpendicular to each other.
- Another major difference is that the diagonals in a rectangle are all of the same lengths, whereas the diagonals in a parallelogram are all of different lengths.
Ques. Calculate the perimeter of a rectangular plot of length of 9m and breadth of 6m? (1 Mark)
Ans. We know that,
Perimeter of Rectangle = 2[l+b]
Perimeter of Rectangular plot= 2[9+6]
Perimeter = 30m
Ques. Calculate the breadth of a rectangle if its length is 10 m and perimeter is 54 m? (2 Marks)
Ans. We know that,
Perimeter of Rectangle = 2[l+b]
Let,
L be the length=10 m
b is the breadth= b m
P be the perimeter of the reactnagle= 54m
54 = 2[10+b]
54 = 20 + 2b
2b = 34
b= 17
Breadth of the rectangle,b = 17m
Ques. Calculate the area of a rectangle if its breadth is 20 m and perimeter is 60 m? (2 Marks)
Ans. We know that,
Perimeter of Rectangle = 2[l+b]
Let,
L be the length=l m
b is the breadth= 20 m
P be the perimeter of the reactnagle= 60m
60 = 2[l+20]
60 = 2l + 40
2l = 20
l = 10 m
We know that,
area of a rectangle = lxb
Area of rectangle = 20 x10
Area = 200 m2
Ques. What are some of the properties of a rectangle? (4 Marks)
Ans. The following are some of the basic properties of a rectangle:
- It's a quadrilateral.
- It has four sides.
- The opposing sides are parallel and equal.
- When the inner angles are summed together, they equal 360°.
- There are two diagonals that bisect each other.
- The diagonals are all the same length.
- The rectangle is a square if the angle at which the diagonals intersect each other is 90°.
Ques. A bedsheet has a length of 120 inches and a breadth of 85 inches. How much lace will be required to complete the border? (2 Marks)
Ans. To calculate the amount of lace needed for the bedsheet's border, we shall use the perimeter of the rectangle formula to get the bedsheet's perimeter.
The length is 120 inches
The breadth is 85 inches.
Perimeter of a rectangle = 2(l + w)
Therefore,
P= 2(l + w)
= 2(120 + 85)
= 2 (205)
= 410 inches
Thus, 410 inches of lace is needed to encircle the bedsheet.
Ques. What is the area of the rectangle? Give the formula for the area of a rectangle? (2 Marks)
Ans. The area of any figure is equal to the number of unit squares enclosed by it. Thus, the area of a rectangle can be defined as the total number of square units that can fit inside the rectangle perimeter. The formula for calculating the area of the rectangle is given by,
Area= (Length x Width) square units
Ques. Calculate the length of the photo frame required for a picture of size 20 cm x 90 cm? (2 Marks)
Ans. We know that,
Perimeter of Rectangle = 2[l+b]
Perimeter of Rectangular picture = 2[20+90]
Length of photo frame required = 220cm
Ques. Calculate the perimeter of a rectangular garden of length of 20m and breadth of 20m? (1 Mark)
Ans. We know that,
Perimeter of Rectangle = 2[l+b]
Perimeter of Rectangular garden = 2[20+20]
Perimeter = 80m
Ques. Calculate the breadth of a rectangle if its length is 10 m and perimeter is 60 m? (2 Marks)
Ans. We know that,
Perimeter of Rectangle = 2[l+b]
Let,
L be the length=10 m
b is the breadth= b m
P be the perimeter of the reactnagle= 54m
60 = 2[10+b]
60 = 20 + 2b
2b = 40
b= 20
Breadth of the rectangle, b = 20 m
Ques. Calculate the area of a rectangle if its breadth is 50 m and perimeter is 100 m? (2 Marks)
Ans. We know that,
Perimeter of Rectangle = 2[l+b]
Let,
L be the length=l m
b is the breadth= 50 m
P be the perimeter of the reactnagle= 100m
100 = 2[l+50]
100 = 2l + 0
2l = 0
l = 00 m
We know that,
area of a rectangle = lxb
Area of rectangle = 0 x10
Area = 0 m2
Ques. Consider a chocolate bar which is made up of equal-sized squares with each side measuring 1 inch. Calculate the perimeter of the rectangular chocolate bar? (3 Marks)
Ans. Since it is known that each little square has all its sides is equal to 1 inch. If we count the sides along the length of the bar, we get its value equal to 6 inches. The sides of rectangle along the width of the bar add up to 2 inches. Therefore, the length of the bar = 6 inches, and the width of the bar = 2 inches. Putting these values in the perimeter of rectangle formula we have:
Perimeter = 2(l + w) = 2 (6 + 2) = 2 × 8 = 16 inches
Therefore, the perimeter of rectangle is 16 inches.
Ques. What is the perimeter of a rectangle with a length of 15 mm and a width of 11 mm? (2 Marks)
Ans. Using the perimeter of rectangle formula, let us find its perimeter. Given, length (l) = 15; width (w) = 11 mm
Perimeter of rectangle = 2(l + w). On substituting the values in the formula, we get, 2(l + w) = 2(15 + 11) = 2 × 26 = 52 mm.
Therefore, the perimeter of the rectangle is 56 mm.
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