We will discuss here how to find the perimeter of a rectangle. We know perimeter of a rectangle is the total length (distance) of the boundary of a rectangle. In a rectangle we know that two opposite sides are equal. So, PQ = SR and PS = QR If PS = l and PQ = b Perimeter of the rectangle = PQ + QR + RS + SP = b +l + b + l = 2b +2l Again, ABCD is a rectangle. We know that the opposite sides of a rectangle are equal. AB = CD = 5 cm and BC = AD = 3 cm So, the perimeter of the rectangle ABCD = AB + BC + CD + AD = 5 cm + 3 cm + 5 cm + 3 cm = 16 cm It can be written as 5 cm + 5 cm + 3 cm + 3 cm = (2 × 5) cm + (2 × 3) cm = 2 (5 + 3) cm = 2 × 8 cm = 16 cm We add length and breadth twice to find the perimeter of a rectangle. Perimeter of a rectangle = 2 (length + breadth) A rectangle is a four sided figure in which ● Opposite sides are equal in length. ● Longer side is called length and shorter side is called breadth. ● All angles are equal to 90° (right angle). In the above figure ABCD is a rectangle. Three children found the perimeter of this rectangle in three different methods. 1st method: Perimeter = 6 cm + 4 cm + 6 cm + 4 cm = 20 cm 2nd method: Perimeter = (2 6 cm) + (2 4 cm) = 12 cm + 8 cm = 20 cm 3rd method: Perimeter = 2 (6 cm + 4 cm) = 2 cm × 10 cm = 20 cm All the three methods gave them the same answer. Perimeter of a rectangle = length + breadth + length + breadth = (2 length) + (2 breadth) = 2 (length + breadth) Word Problems on Perimeter of a Rectangle: Let us consider some of the examples on perimeter of a rectangle: 1. The length of a rectangle is 4 cm and its breadth is 2 cm. Find its perimeter. Solution: Length = 4 cm Breadth = 2 cm Therefore, perimeter of the rectangle = 2 (length + breadth) = 2 (4 + 2) cm = 2 × 6 cm = 12 cm 2. Find the perimeter of the rectangle ABCD whose sides are 6 cm and 5 cm. Solution: The perimeter of the rectangle ABCD = 6 cm + 5 cm + 6 cm + 5cm = 22 cm 3. Find the perimeter of a rectangle whose length is 12 cm and breadth is 8 cm. Solution: Length = 12 cm Breadth = 8 cm Perimeter = 2 (length + breadth) = 2 (12 cm + 8 cm) = 2 × 20 cm = 40 cm 4. A rectangular swimming pool is 9 m long and 4 m broad. Find the area of the swimming pool. Solution: Length of the rectangular swimming pool = 9 m Breadth of the rectangular swimming pool = 4 m Therefore, perimeter of the rectangle swimming pool = 2 (length + breadth) = 2 (9 + 4) m = 2 (13) m = 2 × 13 m = 26 m 5. The length of a rectangle is 4.5 m and the breadth is 1.5 m. Find the perimeter. Solution: Length = 4.5 m Breadth = 1.5 m Perimeter = 2 (length + breadth) = 2 × (4.5 m + 1.5 m) = 2 × 6 m = 12 m Therefore, the perimeter is 12 m. 6. A rectangle display board is measuring 8 m by 6 m. Robert wants to add a ribbon border around the display board. What is the length of ribbon that he will need? If the cost of the ribbon is $ 15 per metre then how much money does Robert needs to buy the ribbon? Solution: Length of the display board = 8 m Breadth of the display board = 6 m Perimeter of the display board = 2(Length + Breadth) = 2(8 + 6) m = 2 × 14 m = 28 m. Cost of ribbon is $15 per metre. Therefore, total cost for 28 m long ribbon = $15 × 28 = $420. Questions and Answers on Perimeter of a Rectangle: 1. Find the perimeter of the rectangles having measurements as follows. (i) length = 11 cm breadth = 9 cm (ii) length = 5 cm breadth = 2 cm (iii) length = 10 cm breadth = 8 cm (iv) length = 15 cm breadth = 2 cm Answer: 1. (i) 40 cm (ii) 14 cm (iii) 36 cm (iv) 34 cm Perimeter of a Rectangle Word Problems 2. A rectangle has a perimeter of 40 cm. If its length is 8 cm, what is its breath? Answer: 2. 12 cm 3. Sam is running around a rectangular park of length 450 m and breadth 300 m. Find the total distance covered by him if he takes 10 rounds of the park. Answer: 3. 15000 m 4. A gardener wants to fence its rectangular garden with a wire. The length and breadth of the garden is 25 m and 16 m respectively. Find the length of the wire he must buy. Answer: 4. 82 m
● Related Concepts ● Units for Measuring Length ● Measuring Instruments ● To Measure the Length of a Line-segment ● Perimeter of a Figure ● Perimeter of a Triangle ● Perimeter of a Rectangle ● Perimeter of a Square ● Unit of Mass or Weight ● Examples on Unit of Mass or Weight ● Units for The Measurement of Capacity ● Examples on Measurement of Capacity ● Measurement of Time ● Read a Watch or a Clock ● Antemeridian (a.m.) or Postmeridian (p.m.) ● What Time it is? ● Time in Hours and Minutes ● 24 Hour Clock ● Units of Time ● Examples Units of Time ● Time Duration ● Calendar ● Reading and Interpreting a Calendar ● Calendar Guides us to Know 4th Grade Math Activities From Perimeter of a Rectangle to HOME PAGE
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