The number of paving stones each measuring `2.5 xx 2m` required to pave a rectangular courtyard 30 m long and 17.5 m wide, is

Options

A. 80
B. 33
C. 99
D. 105

Answer

To find the number of paving stones required to pave a rectangular courtyard, we need to calculate the area of both the courtyard and a single paving stone. Then, we can determine how many paving stones are needed by dividing the area of the courtyard by the area of one paving stone.

### Step-by-Step Solution:

1. **Calculate the area of the rectangular courtyard.**
- The formula for the area of a rectangle is:
\[ \text{Area} = \text{Length} \times \text{Width} \]
- Given:
- Length of the courtyard = 30 m
- Width of the courtyard = 17.5 m
- So, the area of the courtyard is:
\[ \text{Area}_{\text{courtyard}} = 30 \, \text{m} \times 17.5 \, \text{m} = 525 \, \text{m}^2 \]

2. **Calculate the area of one paving stone.**
- The dimensions of the paving stone are:
- Length = 2.5 m
- Width = 2 m
- Using the area formula for the stone:
\[ \text{Area}_{\text{stone}} = 2.5 \, \text{m} \times 2 \, \text{m} = 5 \, \text{m}^2 \]

3. **Determine the number of paving stones required.**
- To find the number of paving stones, divide the area of the courtyard by the area of one paving stone:
\[ \text{Number of paving stones} = \frac{\text{Area}_{\text{courtyard}}}{\text{Area}_{\text{stone}}} = \frac{525 \, \text{m}^2}{5 \, \text{m}^2} = 105 \]

### Final Answer:
The number of paving stones required to pave the rectangular courtyard is **105**.

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