Question 55: Find the Breadth of a Rectangle

Q: A square and a rectangle have the same perimeter. If the side of the square is 16 m and the length of the rectangle is 18 m, find the breadth of the rectangle.

Options:
(a) 14 m
(b) 15 m
(c) 16 m
(d) 17 m

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📝 Step-by-Step Solution

Step 1: Understand the problem

We have:

• Square side = 16 m

• Rectangle length = 18 m

• Both shapes have the same perimeter

• Find rectangle breadth

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Step 2: Recall formulas

1. Perimeter of a square = 4 × side

2. Perimeter of a rectangle = 2 × (length + breadth)

💡 Tip: Perimeter = total distance around the shape.

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Step 3: Find the square's perimeter

$$P_\text{square} = 4 \times 16 = 64 \text{ m}$$

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Step 4: Set up the rectangle’s perimeter

$$P_\text{rectangle} = 2 \times (\text{length} + \text{breadth})$$

Since both perimeters are equal:

$$2 \times (18 + \text{breadth}) = 64$$

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Step 5: Solve for breadth

1. Divide both sides by 2:

$$18 + \text{breadth} = 32$$

2. Subtract 18 from both sides:

$$\text{breadth} = 32 - 18 = 14$$

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✅ Step 6: Answer

The breadth of the rectangle = 14 m

Correct option: (a) 14 m

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Quick Tip for Similar Problems

1. Write perimeter formulas.

2. Plug in known values.

3. Solve step by step.

4. Check your answer by comparing perimeters.

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💡 Fun Analogy:
Imagine reshaping a square chocolate bar into a rectangle while keeping the wrapper same. The wrapper = perimeter, so if the length stretches, the breadth must shrink to fit the wrapper perfectly! 🍫