Floor of a square room of side 10 m is to be completely covered with square tiles, each having length 50 cm. The smallest number of tiles needed is

Options

A. 200
B. 300
C. 400
D. 500

Answer

To solve the problem of determining the smallest number of square tiles needed to cover the floor of a square room, we can follow these steps:

### Step 1: Determine the area of the room
The room is square with a side length of 10 meters. The area \( A \) of a square is calculated using the formula:
\[ A = \text{side}^2 \]
So, the area of the room is:
\[ A = 10 \, \text{m} \times 10 \, \text{m} = 100 \, \text{m}^2 \]

### Step 2: Convert the area of the room to square centimeters
Since the tiles are measured in centimeters, we need to convert the area of the room from square meters to square centimeters. There are 10,000 square centimeters in a square meter (since \( 1 \, \text{m} = 100 \, \text{cm} \)):
\[ 100 \, \text{m}^2 = 100 \times 10,000 \, \text{cm}^2 = 1,000,000 \, \text{cm}^2 \]

### Step 3: Determine the area of one tile
Each tile is a square with a side length of 50 cm. The area \( A_t \) of one tile is:
\[ A_t = \text{side}^2 = 50 \, \text{cm} \times 50 \, \text{cm} = 2500 \, \text{cm}^2 \]

### Step 4: Calculate the number of tiles needed
To find the number of tiles required to cover the entire area of the room, we divide the area of the room by the area of one tile:
\[ \text{Number of tiles} = \frac{\text{Area of the room}}{\text{Area of one tile}} = \frac{1,000,000 \, \text{cm}^2}{2500 \, \text{cm}^2} \]
Calculating this gives:
\[ \text{Number of tiles} = 400 \]

### Conclusion
The smallest number of tiles needed to cover the floor of the room is **400 tiles**.

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