How many marble tiles of `12 cm xx 3 cm` will be needed to fit in a rectangular region of length 90 cm and breadth 40 cm ?

Answer

To determine how many marble tiles of size \(12 \, \text{cm} \times 3 \, \text{cm}\) are needed to fit in a rectangular region of length \(90 \, \text{cm}\) and breadth \(40 \, \text{cm}\), we can follow these steps:

### Step 1: Calculate the area of the rectangular region.
The area \(A\) of a rectangle is calculated using the formula:
\[ A = \text{length} \times \text{breadth} \]
Given:
- Length = \(90 \, \text{cm}\)
- Breadth = \(40 \, \text{cm}\)

Calculating the area:
\[ A = 90 \, \text{cm} \times 40 \, \text{cm} = 3600 \, \text{cm}^2 \]

### Step 2: Calculate the area of one marble tile.
The area \(A_t\) of a tile is calculated using the same formula:
\[ A_t = \text{length} \times \text{breadth} \]
Given:
- Length of tile = \(12 \, \text{cm}\)
- Breadth of tile = \(3 \, \text{cm}\)

Calculating the area of one tile:
\[ A_t = 12 \, \text{cm} \times 3 \, \text{cm} = 36 \, \text{cm}^2 \]

### Step 3: Calculate the number of tiles needed.
To find the number of tiles required, divide the area of the rectangular region by the area of one tile:
\[ \text{Number of tiles} = \frac{\text{Area of rectangular region}}{\text{Area of one tile}} = \frac{3600 \, \text{cm}^2}{36 \, \text{cm}^2} \]

Calculating the number of tiles:
\[ \text{Number of tiles} = 100 \]

### Final Answer:
You will need **100 marble tiles** of size \(12 \, \text{cm} \times 3 \, \text{cm}\) to fit in the rectangular region of \(90 \, \text{cm} \times 40 \, \text{cm}\).

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