Example 1. A rectangle is 15 cm long and 8 cm wide. Find its perimeter.
- .
- .
Answer: 46 cm
Perimeter of a rectangle
The perimeter of a rectangle is the total distance around its edge. A rectangle has two equal lengths and two equal widths, so you add one length and one width and double the result.
Formulas
Perimeter of a rectangle
Missing width (when the perimeter and length are known)
Perimeter of a square
Worked examples
Example 2. The perimeter of a rectangle is 56 m and its length is 18 m. Find its width.
- Half the perimeter is , which is length + width.
- Width = .
Answer: 10 m
Example 3. A garden is 20 m by 12 m. It is fenced all round, with a 2 m gap left for a gate. How much fencing is needed?
- Perimeter = m.
- Take away the gate: .
Answer: 62 m
Common mistakes
- Multiplying length by width. That gives the area, not the perimeter.
- Adding only two sides. A rectangle has four sides, so double the sum of one length and one width.
- Writing square units for a perimeter. Perimeter is a length, so cm or m, not .
Practice questions with answers
1. What is the perimeter of a square of side 5 cm?
- A10 cm
- B20 cm
- C25 cm
- D15 cm
Show answer
Answer: B) 20 cm
Perimeter of a square = 4 × side = cm.
2. Riya's square handkerchief has each side 25 cm. What is its perimeter?
- A50 cm
- B75 cm
- C100 cm
- D625 cm
Show answer
Answer: C) 100 cm
Perimeter of a square = 4 × side = cm.
3. Find the cost of fencing a square field of side 35 m at the rate of Rs 12 per metre (answer in rupees).
- A1680
- B1850
- C1510
- D3360
Show answer
Answer: A) 1680
Perimeter = m. Cost = = Rs 1680.
4. A village has a triangular park whose sides are in the ratio 3 : 4 : 5.
The perimeter of the park is 96 m.
What is the length of its longest side?
The perimeter of the park is 96 m.
What is the length of its longest side?
- A40
- B36
- C44
- D80
Show answer
Answer: A) 40
Ratio parts = 3 + 4 + 5 = 12. One part = 96 ÷ 12 = 8 m. Longest side = m.
5. A square field has a perimeter of 360 m.
Fencing the boundary costs ₹8 per metre. What is the cost of fencing the boundary?
Fencing the boundary costs ₹8 per metre. What is the cost of fencing the boundary?
- A₹2880
- B₹720
- C₹5760
- D₹360
Show answer
Answer: A) ₹2880
Only the boundary is charged. Boundary length = perimeter = 360 m. Cost = = ₹2880.
6. A 72 cm long wire is bent to form a rectangle whose length is twice its breadth. Find the LENGTH of that rectangle (in cm).
- A12
- B36
- C48
- D24
Show answer
Answer: D) 24
The wire becomes the perimeter, so → . With → cm and cm. Answering 12 gives the BREADTH; 36 is only the half-perimeter.
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Practice by class
- Class 6 · Perimeter of Shapes60 practice questions with answers
- Class 6 · Perimeter Word Problems60 practice questions with answers
- Class 7 · Perimeter and Area100 practice questions with answers
Frequently asked questions
What is the formula for the perimeter of a rectangle?
, or equivalently .
Can two rectangles have the same perimeter but different areas?
Yes. A 10 cm by 2 cm rectangle and a 6 cm by 6 cm square both have perimeter 24 cm, but their areas are and .
How do you find the perimeter of a square?
Multiply one side by 4: . A square of side 9 cm has perimeter 36 cm.
What unit is perimeter measured in?
Ordinary length units such as mm, cm, m or km, not square units.