Perimeter Word Problems (Grade 5)
Perimeter word problems require you to apply perimeter formulas to real-life situations like fencing a garden, framing a picture, building a boundary wall, or laying a border around a field.
The perimeter is the total length of the boundary of a shape. In Class 5, you will solve multi-step perimeter problems involving rectangles, squares, and composite shapes. You will also find missing dimensions when the perimeter is given.
These problems test your ability to read carefully, extract dimensions, and choose the correct formula.
What is Perimeter Word Problems - Class 5 Maths (Measurement)?
The perimeter of a closed shape is the total distance around its boundary.
Key formulas:
- Perimeter of rectangle = 2 × (length + breadth)
- Perimeter of square = 4 × side
- Perimeter of any shape = sum of all sides
Perimeter Word Problems (Grade 5) Formula
Perimeter of Rectangle = 2 × (Length + Breadth)
Perimeter of Square = 4 × Side
Cost of fencing = Perimeter × Rate per metre
Types and Properties
Common types of perimeter word problems:
- Fencing a garden: Find how much wire or fencing is needed.
- Framing a picture: Find the length of frame needed for a photo or painting.
- Boundary walls: Calculate the length of a boundary wall around a plot.
- Cost of fencing: Multiply perimeter by the rate per metre.
- Finding missing sides: Given the perimeter and one dimension, find the other.
- Composite perimeters: Find the perimeter of L-shaped or other combined shapes.
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 to go around it.
Solution:
Step 1: Perimeter = 2 × (25 + 15) = 2 × 40 = 80 m
Answer: 80 m of fencing is needed.
Example 2: Example 2: Cost of Fencing
Problem: A square park has a side of 30 m. Fencing costs ₹45 per metre. Find the total cost.
Solution:
Step 1: Perimeter = 4 × 30 = 120 m
Step 2: Cost = 120 × 45 = ₹5,400
Answer: The total cost is ₹5,400.
Example 3: Example 3: Finding Missing Breadth
Problem: A rectangular field has a perimeter of 120 m and length 35 m. Find the breadth.
Solution:
Step 1: Perimeter = 2 × (L + B)
Step 2: 120 = 2 × (35 + B)
Step 3: 60 = 35 + B
Step 4: B = 60 − 35 = 25 m
Answer: The breadth is 25 m.
Example 4: Example 4: Framing a Picture
Problem: Aditi wants to frame a rectangular photo that is 30 cm × 20 cm. What length of frame strip does she need?
Solution:
Step 1: Perimeter = 2 × (30 + 20) = 2 × 50 = 100 cm
Answer: Aditi needs 100 cm (1 m) of frame strip.
Example 5: Example 5: Running Around a Track
Problem: Rahul runs 4 rounds around a rectangular playground that is 50 m long and 30 m wide. What total distance does he cover?
Solution:
Step 1: Perimeter = 2 × (50 + 30) = 160 m
Step 2: Total distance = 4 × 160 = 640 m
Answer: Rahul covers 640 m.
Example 6: Example 6: Finding Side of a Square
Problem: A square garden has a perimeter of 84 m. Find its side.
Solution:
Step 1: Perimeter = 4 × side
Step 2: 84 = 4 × side
Step 3: side = 84 ÷ 4 = 21 m
Answer: The side is 21 m.
Example 7: Example 7: Ribbon Around a Gift
Problem: Meera wraps a ribbon once around a square gift box with a side of 18 cm. She needs an extra 15 cm for the bow. What total length of ribbon does she need?
Solution:
Step 1: Perimeter = 4 × 18 = 72 cm
Step 2: Total ribbon = 72 + 15 = 87 cm
Answer: Meera needs 87 cm of ribbon.
Example 8: Example 8: Fencing with a Gate
Problem: A rectangular plot is 40 m × 25 m. A gate of 3 m width is left open. Find the length of fencing needed.
Solution:
Step 1: Full perimeter = 2 × (40 + 25) = 130 m
Step 2: Fencing needed = 130 − 3 = 127 m
Answer: 127 m of fencing is needed.
Example 9: Example 9: Wire Bent into a Rectangle
Problem: A wire 64 cm long is bent into a rectangle. If the length is 20 cm, find the breadth.
Solution:
Step 1: Wire length = perimeter = 64 cm
Step 2: 64 = 2 × (20 + B)
Step 3: 32 = 20 + B
Step 4: B = 12 cm
Answer: The breadth is 12 cm.
Example 10: Example 10: Comparing Perimeters
Problem: Rectangle A is 12 m × 8 m. Rectangle B is 15 m × 5 m. Which has a greater perimeter?
Solution:
A: 2 × (12 + 8) = 40 m
B: 2 × (15 + 5) = 40 m
Answer: Both have the same perimeter (40 m), even though they have different shapes.
Key Points to Remember
- Perimeter = total distance around the boundary of a shape.
- Rectangle perimeter = 2(L + B). Square perimeter = 4 × side.
- Cost of fencing = perimeter × rate per metre.
- If a gate or opening is present, subtract the opening width from the perimeter.
- To find a missing dimension: rearrange the perimeter formula.
- For multiple rounds: total distance = perimeter × number of rounds.
- Different rectangles can have the same perimeter but different areas.
- Always check that units are consistent before calculating.
Practice Problems
- A rectangular park is 45 m long and 30 m wide. Find the perimeter.
- A square field has a perimeter of 100 m. Find the length of one side.
- Kavi fences a rectangular plot of 50 m × 35 m. Fencing costs ₹60 per metre. Find the total cost.
- A rectangle has a perimeter of 56 cm and length 18 cm. Find the breadth.
- Arjun runs 3 laps around a rectangular field of 80 m × 60 m. How far does he run?
- Neha frames a square painting with side 25 cm. She buys 120 cm of frame strip. Is it enough?
- A rectangular garden 35 m × 20 m has two gates, each 2 m wide. Find the fencing needed.
- A wire 48 cm long is bent into a square. Find the side length of the square.
Frequently Asked Questions
Q1. What is perimeter?
Perimeter is the total length of the boundary of a closed shape. It tells you how far you would walk if you went all the way around the shape.
Q2. What is the formula for the perimeter of a rectangle?
Perimeter of rectangle = 2 × (length + breadth). You add the length and breadth, then multiply by 2.
Q3. How do I find a missing side from the perimeter?
For a rectangle: breadth = (perimeter ÷ 2) − length. For a square: side = perimeter ÷ 4.
Q4. How is perimeter different from area?
Perimeter measures the boundary (in metres or cm). Area measures the surface enclosed (in square metres or cm²). Different shapes can have the same perimeter but different areas.
Q5. How do you calculate the cost of fencing?
First find the perimeter. Then multiply: cost = perimeter × rate per metre. If there is a gate, subtract the gate width from the perimeter first.
Q6. What if the shape is not a rectangle?
For any polygon, the perimeter is the sum of all its sides. Add up each side length.
Q7. Can two rectangles have the same perimeter but different areas?
Yes. For example, a 10 m × 5 m rectangle and a 8 m × 7 m rectangle both have perimeter 30 m, but areas 50 m² and 56 m² respectively.
Q8. How do I handle fencing with a gate?
Calculate the full perimeter first, then subtract the width of the gate. The remaining length is the fencing needed.
Q9. Is this topic in the NCERT Class 5 syllabus?
Yes. Perimeter word problems involving rectangles and squares are part of the Measurement chapter in NCERT/CBSE Class 5 Maths.
