Perimeter of Rectangle
A rectangle has two pairs of equal sides -- two lengths and two breadths. The perimeter of a rectangle is the total distance around it.
In Class 3, students learn the formula for the perimeter of a rectangle and apply it to word problems involving gardens, rooms, picture frames, and more.
What is Perimeter of Rectangle - Class 3 Maths (Geometry)?
The perimeter of a rectangle is the sum of all four sides.
Perimeter of Rectangle = 2 × (Length + Breadth)
This can also be written as: Perimeter = Length + Breadth + Length + Breadth.
Perimeter of Rectangle Formula
P = 2 × (L + B)
Where L = length and B = breadth of the rectangle.
Solved Examples
Example 1: Basic Perimeter Calculation
Question: Find the perimeter of a rectangle with length 10 cm and breadth 5 cm.
Think:
- P = 2 × (L + B)
- P = 2 × (10 + 5)
- P = 2 × 15 = 30 cm
Answer: The perimeter is 30 cm.
Example 2: Fencing a Rectangular Garden
Question: Ria's rectangular garden is 12 m long and 8 m wide. How much fencing does she need?
Think:
- Fencing = perimeter
- P = 2 × (12 + 8) = 2 × 20 = 40 m
Answer: Ria needs 40 m of fencing.
Example 3: Ribbon Around a Photo Frame
Question: A rectangular photo frame is 25 cm long and 15 cm wide. How much ribbon is needed to go around it?
Think:
- P = 2 × (25 + 15) = 2 × 40 = 80 cm
Answer: 80 cm of ribbon is needed.
Example 4: Finding Breadth from Perimeter
Question: A rectangle has a perimeter of 36 cm and a length of 12 cm. Find the breadth.
Think:
- P = 2 × (L + B)
- 36 = 2 × (12 + B)
- 18 = 12 + B
- B = 18 − 12 = 6 cm
Answer: The breadth is 6 cm.
Example 5: Finding Length from Perimeter
Question: A rectangular playground has a perimeter of 100 m. The breadth is 20 m. Find the length.
Think:
- 100 = 2 × (L + 20)
- 50 = L + 20
- L = 50 − 20 = 30 m
Answer: The length is 30 m.
Example 6: Perimeter of a Classroom Blackboard
Question: Aman's classroom blackboard is 3 m long and 1 m wide. Find its perimeter.
Think:
- P = 2 × (3 + 1) = 2 × 4 = 8 m
Answer: The perimeter of the blackboard is 8 m.
Example 7: Cost of Fencing
Question: Dev wants to fence a rectangular field that is 15 m long and 10 m wide. Fencing costs ₹5 per metre. What is the total cost?
Think:
- P = 2 × (15 + 10) = 2 × 25 = 50 m
- Total cost = 50 × ₹5 = ₹250
Answer: The total cost is ₹250.
Example 8: Comparing Perimeters of Two Rectangles
Question: Rectangle A has length 9 cm and breadth 4 cm. Rectangle B has length 7 cm and breadth 6 cm. Which has a larger perimeter?
Think:
- P(A) = 2 × (9 + 4) = 2 × 13 = 26 cm
- P(B) = 2 × (7 + 6) = 2 × 13 = 26 cm
Answer: Both rectangles have the same perimeter of 26 cm.
Example 9: Perimeter on a Grid
Question: A rectangle on a 1-cm grid is 6 squares long and 3 squares wide. Find its perimeter.
Think:
- Length = 6 cm, Breadth = 3 cm
- P = 2 × (6 + 3) = 2 × 9 = 18 cm
Answer: The perimeter is 18 cm.
Key Points to Remember
- A rectangle has 2 lengths and 2 breadths.
- Perimeter = 2 × (Length + Breadth).
- Perimeter is measured in cm, m, or other length units.
- If perimeter and one side are known, the other side can be found using subtraction.
- Perimeter is used for fencing, bordering, and framing rectangular shapes.
- Two different rectangles can have the same perimeter but different lengths and breadths.
Practice Problems
- Find the perimeter of a rectangle with length 14 cm and breadth 7 cm.
- A rectangular park is 50 m long and 30 m wide. What is its perimeter?
- Priya puts border tape around a rectangular chart paper that is 60 cm long and 40 cm wide. How much tape does she need?
- A rectangle has a perimeter of 28 cm and a length of 9 cm. Find the breadth.
- Meera's rectangular terrace is 8 m long and 5 m wide. How much railing is needed to go around it?
- A rectangle has a perimeter of 50 m. The breadth is 10 m. Find the length.
- Fencing costs ₹8 per metre. What is the cost of fencing a rectangular plot that is 20 m long and 12 m wide?
Frequently Asked Questions
Q1. What is the formula for the perimeter of a rectangle?
Perimeter of a rectangle = 2 multiplied by (Length + Breadth), or P = 2 x (L + B).
Q2. Why do we multiply by 2 in the rectangle perimeter formula?
A rectangle has two lengths and two breadths. Adding L + B gives half the perimeter (one length and one breadth). Multiplying by 2 accounts for both pairs.
Q3. How do you find the breadth if perimeter and length are given?
Use the formula: Breadth = (Perimeter divided by 2) minus Length. For example, if P = 24 cm and L = 8 cm, then B = (24 / 2) - 8 = 12 - 8 = 4 cm.
Q4. What is the unit of perimeter?
Perimeter is measured in the same unit as the sides. If sides are in cm, perimeter is in cm. If sides are in metres, perimeter is in metres.
Q5. Can two different rectangles have the same perimeter?
Yes. For example, a rectangle 8 cm x 2 cm has perimeter 20 cm, and a rectangle 6 cm x 4 cm also has perimeter 20 cm.
Q6. Where is perimeter of a rectangle used in daily life?
It is used for fencing gardens, putting borders on charts, framing pictures, building walls around a rectangular plot, and calculating the length of wire needed.
Q7. Is a square a special rectangle?
Yes. A square is a rectangle where all four sides are equal. The perimeter formula still works: P = 2 x (side + side) = 4 x side.
Q8. Is perimeter of rectangle covered in NCERT Class 3?
Yes. The perimeter of a rectangle is covered in the Geometry chapter of NCERT Class 3 Maths. Students learn the formula and solve word problems.
