Word Problems on Perimeter
You already know how to find the perimeter of rectangles, squares, and triangles. Now it is time to use those skills in real-life word problems.
Perimeter is the total distance around a shape. Whenever you need to find how much fencing to put around a garden, how much lace to sew around a handkerchief, or how much wire to bend into a frame — you are calculating perimeter.
Word problems on perimeter test whether you can apply formulas to practical situations. Read carefully, draw a diagram if needed, and solve step by step.
What is Word Problems on Perimeter?
Perimeter Formulas:
- Rectangle: P = 2 × (length + width)
- Square: P = 4 × side
- Triangle: P = side₁ + side₂ + side₃
- Any shape: P = sum of all sides
Steps for word problems:
- Read the problem and identify the shape.
- Write down the known dimensions.
- Decide what is asked — perimeter, or a missing side from given perimeter.
- Apply the correct formula.
- Write the answer with the unit (cm, m, km).
Types and Properties
1. Finding Perimeter (Direct Problems)
Given all sides, find the perimeter by adding them up.
2. Finding a Missing Side (Reverse Problems)
Given the perimeter and some sides, find the unknown side.
- Missing side = Perimeter − sum of known sides.
3. Cost Problems
Find the perimeter, then multiply by the cost per unit length.
- Cost of fencing = Perimeter × rate per metre.
4. Wire Bending Problems
A wire of a given length is bent into a shape. The wire length equals the perimeter of the shape.
Solved Examples
Example 1: Example 1: Fencing a rectangular garden
Problem: A rectangular garden is 25 m long and 15 m wide. Find the length of fencing needed.
Solution:
- P = 2(25 + 15) = 2 × 40 = 80 m
Answer: 80 m of fencing is needed.
Example 2: Example 2: Cost of fencing
Problem: A square field has side 30 m. Fencing costs Rs. 12 per metre. Find the total cost.
Solution:
- P = 4 × 30 = 120 m.
- Cost = 120 × 12 = Rs. 1,440.
Answer: Rs. 1,440
Example 3: Example 3: Finding missing side of rectangle
Problem: A rectangle has perimeter 56 cm and length 18 cm. Find the width.
Solution:
- P = 2(l + w) → 56 = 2(18 + w) → 28 = 18 + w → w = 10 cm.
Answer: Width = 10 cm
Example 4: Example 4: Triangular plot
Problem: A triangular plot has sides 20 m, 30 m, and 40 m. Find the perimeter. If fencing costs Rs. 50 per metre, find total cost.
Solution:
- P = 20 + 30 + 40 = 90 m.
- Cost = 90 × 50 = Rs. 4,500.
Answer: Perimeter = 90 m. Cost = Rs. 4,500.
Example 5: Example 5: Wire bending into square
Problem: A wire is 48 cm long. It is bent into a square. Find the side of the square.
Solution:
- Wire length = Perimeter of square = 48 cm.
- Side = 48 ÷ 4 = 12 cm.
Answer: Side = 12 cm
Example 6: Example 6: Wire bent into rectangle
Problem: A 60 cm wire is bent into a rectangle with length 18 cm. Find the width.
Solution:
- Perimeter = 60 cm.
- 60 = 2(18 + w) → 30 = 18 + w → w = 12 cm.
Answer: Width = 12 cm
Example 7: Example 7: Lace around a handkerchief
Problem: A square handkerchief has side 25 cm. How much lace is needed to go around it?
Solution:
- P = 4 × 25 = 100 cm = 1 m.
Answer: 100 cm (1 metre) of lace.
Example 8: Example 8: Perimeter of irregular shape
Problem: A field has 5 sides: 12 m, 8 m, 15 m, 10 m, and 5 m. Find the perimeter.
Solution:
- P = 12 + 8 + 15 + 10 + 5 = 50 m.
Answer: 50 m
Example 9: Example 9: Running track
Problem: A rectangular field is 100 m × 60 m. Raj runs around it 3 times. How much does he run?
Solution:
- P = 2(100 + 60) = 320 m.
- 3 rounds = 3 × 320 = 960 m.
Answer: Raj runs 960 m.
Example 10: Example 10: Comparing perimeters
Problem: Square A has side 10 cm. Rectangle B is 14 cm × 6 cm. Which has a larger perimeter?
Solution:
- Square: P = 4 × 10 = 40 cm.
- Rectangle: P = 2(14 + 6) = 40 cm.
Answer: Both have equal perimeters of 40 cm.
Real-World Applications
Fencing: Farmers and gardeners calculate perimeter to know how much fencing wire or railing to buy.
Framing: Picture frames, photo frames, and window frames require perimeter measurement to cut the right length of material.
Sewing: Adding lace, ribbon, or piping around a cloth item (handkerchief, tablecloth) needs perimeter calculation.
Sports: Running tracks, cricket boundaries, and football field markings are all based on perimeter.
Construction: Laying tiles along the edge of a room, or painting the border of a wall, requires knowing the perimeter.
Key Points to Remember
- Perimeter = total length around a shape = sum of all sides.
- Rectangle: P = 2(l + w). Square: P = 4s. Triangle: P = a + b + c.
- When a wire is bent into a shape, wire length = perimeter of the shape.
- To find a missing side: subtract known sides from the perimeter.
- Cost of fencing = Perimeter × rate per metre.
- Perimeter is measured in units of length (cm, m, km), NOT square units.
- Draw a diagram to help visualise the problem.
- Always include the unit in your answer.
Practice Problems
- A rectangular park is 80 m × 50 m. Find the total distance covered in 5 rounds.
- A square room has perimeter 52 m. Find the side.
- A wire 72 cm long is bent into an equilateral triangle. Find the side.
- Fencing a rectangular plot 45 m × 30 m costs Rs. 25 per metre. Find the total cost.
- A triangle has perimeter 42 cm. Two sides are 14 cm and 16 cm. Find the third side.
- A rectangular garden 20 m × 10 m has a gate 3 m wide (no fencing at the gate). How much fencing is needed?
- A wire is bent into a rectangle 15 cm × 10 cm. If the same wire is bent into a square, what is the side of the square?
- Which needs more fencing: a square field of side 25 m or a rectangular field 30 m × 20 m?
Frequently Asked Questions
Q1. What is perimeter?
Perimeter is the total distance around the boundary of a flat shape. It is the sum of all the sides.
Q2. What is the difference between perimeter and area?
Perimeter is the length around a shape (measured in cm, m). Area is the space inside a shape (measured in cm², m²). Perimeter is 1-dimensional; area is 2-dimensional.
Q3. How do I find a missing side if perimeter is given?
Subtract the sum of known sides from the perimeter. For a rectangle: width = (Perimeter/2) − length.
Q4. If a wire is bent into different shapes, does the perimeter change?
No. The wire length stays the same, so the perimeter stays the same. Only the shape changes.
Q5. Can two different shapes have the same perimeter?
Yes. A square of side 10 cm (P = 40 cm) and a rectangle of 14 cm × 6 cm (P = 40 cm) have the same perimeter but different shapes and areas.
Q6. How do I find the cost of fencing?
First find the perimeter. Then multiply by the cost per metre: Total cost = Perimeter × rate per metre.
Q7. What if the shape has a gate or opening?
Subtract the width of the gate from the perimeter. Fencing needed = Perimeter − gate width.
Q8. What unit is perimeter measured in?
Perimeter is measured in units of length: cm, m, km. NOT in square units (those are for area).
