Problem Set 49 – Perimeter Formulas and Word ProblemsClass 5 Maths · Chapter 12 Perimeter and Area · Problem Set 49 – Maharashtra Board

Summary: Problem Set 49 – Perimeter Formulas and Word Problems

A rectangle has two lengths and two breadths, so its perimeter = 2 × length + 2 × breadth.

A square has four equal sides, so its perimeter = 4 × length of one side.

Going once round a field covers its perimeter. Going round several times means multiplying the perimeter by the number of rounds.

A double or triple fence needs 2 or 3 times the perimeter of wire. Cost = length of wire × cost of 1 metre.

Change long distances into kilometres: 1000 m = 1 km, so 4800 m = 4 km 800 m.

Key points to remember

• Rectangle: P = 2 × length + 2 × breadth
• Square: P = 4 × side
• Triangle: add the 3 sides
• One round = one perimeter
• n rounds = n × perimeter
• Triple fence = 3 × perimeter
• Cost = metres of wire × rate per metre
• 1000 m = 1 km

Problem Set 49 – Perimeter Formulas and Word Problems – Notes

1. Rule for a rectangle

• Perimeter = length + breadth + length + breadth.
• Since the length comes twice and the breadth comes twice: perimeter = 2 × length + 2 × breadth.
• Rectangle 8 cm by 5 cm: 2 × 8 + 2 × 5 = 16 + 10 = 26 cm.

2. Rule for a square

• All four sides are equal, so perimeter = 4 × side.
• Square of side 11 cm: 4 × 11 = 44 cm.
• Going backwards: a square with perimeter 48 m has side 48 ÷ 4 = 12 m.

3. Rounds and running

• Running once round a park = covering its perimeter once.
• A square park of side 150 m has perimeter 4 × 150 = 600 m.
• 8 rounds: 600 × 8 = 4800 m = 4 km 800 m.

4. Fences and their cost

• A single fence around a field uses wire equal to the perimeter.
• Double fence → 2 × perimeter; triple fence → 3 × perimeter; four rounds → 4 × perimeter.
• Then multiply by the price of one metre to get the total cost.

5. Triangles with decimals

• For a triangle, just add the three sides, even if they are decimals.
• Line up the decimal points: 12.5 + 9.3 + 8.2 = 30.0 cm.
• Wire to bend into a shape = perimeter of that shape.

Formulas at a glance

Key terms

Problem Set 49 – Perimeter Formulas and Word Problems – Flashcards

Read the question, answer it in your head, then tap the card to check. 10 cards.

Problem Set 49 – Perimeter Formulas and Word Problems – MCQ Quiz

10 questions. Tap an option — you will see at once if it is right and why.

How to study Problem Set 49 – Perimeter Formulas and Word Problems

⏱ About 25 minutes

1. Learn (5 min)
   Write the two rules: rectangle 2 × l + 2 × b, square 4 × side.
2. Solve (15 min)
   Solve one rounds problem and one fence-cost problem step by step.
3. Practise (5 min)
   Do the 4 'Try it yourself' problems, take the quiz and play 🎮 Play.