If the ratio of the length to the breadth of a rectangular wall is $2:1$ and the perimeter of the wall is $348$ meters, approximately how many bricks of size $4 ext{ m} imes 3 ext{ m}$ are needed to cover the wall?

Question

If the ratio of the length to the breadth of a rectangular wall is $2:1$ and the perimeter of the wall is $348$ meters, approximately how many bricks of size $4 	ext{ m} 	imes 3 	ext{ m}$ are needed to cover the wall?

Accepted Answer

**Solution:**

1. Let the length be $2x$ and the breadth be $x$.

2. The perimeter of a rectangle is given by:
   $$P = 2(	ext{length} + 	ext{breadth})$$

3. Substitute the values:
   $$348 = 2(2x + x) = 2(3x) = 6x$$

4. Solve for $x$:
   $$x = \frac{348}{6} = 58$$

5. Therefore,
   - Length = $2x = 2 	imes 58 = 116$ meters
   - Breadth = $x = 58$ meters

6. Calculate the area of the wall:
   $$	ext{Area} = 	ext{length} 	imes 	ext{breadth} = 116 	imes 58 = 6728 	ext{ m}^2$$

7. Area of one brick:
   $$4 	ext{ m} 	imes 3 	ext{ m} = 12 	ext{ m}^2$$

8. Number of bricks required:
   $$\frac{6728}{12} \approx 560.67$$

9. Since the number of bricks must be whole, approximately $561$ bricks are needed.

**Answer:** 561

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