Square tiles of side 20 cm are to be laid on the floor of a room 10 m by 4.5 m . How many tiles will be needed ? Find the cost of putting the tiles at Rs. 131 .40 per tile .

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Convert the dimensions of the room from meters to centimeters.
- The dimensions of the room are given as 10 m by 4.5 m.
- We know that 1 meter = 100 centimeters.
- Therefore, we convert:
- Length: \( 10 \, \text{m} = 10 \times 100 = 1000 \, \text{cm} \)
- Breadth: \( 4.5 \, \text{m} = 4.5 \times 100 = 450 \, \text{cm} \)

### Step 2: Calculate the area of the room.
- The area of a rectangle is calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
- Substituting the values:
\[ \text{Area of the room} = 1000 \, \text{cm} \times 450 \, \text{cm} = 450000 \, \text{cm}^2 \]

### Step 3: Calculate the area of one tile.
- The side of the square tile is given as 20 cm.
- The area of a square is calculated using the formula:
\[ \text{Area} = \text{side}^2 \]
- Substituting the value:
\[ \text{Area of one tile} = 20 \, \text{cm} \times 20 \, \text{cm} = 400 \, \text{cm}^2 \]

### Step 4: Calculate the number of tiles needed.
- The number of tiles required can be calculated by dividing the area of the room by the area of one tile:
\[ \text{Number of tiles} = \frac{\text{Area of the room}}{\text{Area of one tile}} = \frac{450000 \, \text{cm}^2}{400 \, \text{cm}^2} \]
- Performing the division:
\[ \text{Number of tiles} = 1125 \]

### Step 5: Calculate the total cost of the tiles.
- The cost of one tile is given as Rs. 131.40.
- To find the total cost, we multiply the number of tiles by the cost per tile:
\[ \text{Total cost} = \text{Number of tiles} \times \text{Cost per tile} = 1125 \times 131.40 \]
- Performing the multiplication:
\[ \text{Total cost} = 147825 \]

### Final Answer:
- The total number of tiles needed is **1125**.
- The total cost of putting the tiles is **Rs. 147825**.

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