The length and breadth ofa room are 15 m 17 cm and 9 m 2 cm respectively. How many, squarical tiles will cover the area of the floor of this room (minimum).

Options

A. 258
B. 837
C. 814
D. 899

Answer

To solve the problem of how many square tiles will cover the area of the floor of the room, we will follow these steps:

### Step 1: Convert the dimensions of the room to centimeters.
- The length of the room is given as 15 m 17 cm.
- Convert 15 m to cm: \( 15 \text{ m} = 15 \times 100 = 1500 \text{ cm} \)
- Therefore, the total length in cm is:
\[ 1500 \text{ cm} + 17 \text{ cm} = 1517 \text{ cm} \]

- The breadth of the room is given as 9 m 2 cm.
- Convert 9 m to cm: \( 9 \text{ m} = 9 \times 100 = 900 \text{ cm} \)
- Therefore, the total breadth in cm is:
\[ 900 \text{ cm} + 2 \text{ cm} = 902 \text{ cm} \]

### Step 2: Calculate the area of the room.
- The area of the room can be calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
- Substituting the values we found:
\[ \text{Area} = 1517 \text{ cm} \times 902 \text{ cm} \]
- Performing the multiplication:
\[ \text{Area} = 1361134 \text{ cm}^2 \]

### Step 3: Determine the size of the square tiles.
- We need to find the side length of the square tiles. The side length is the HCF of the length and breadth of the room.
- To find the HCF of 1517 and 902, we can use the prime factorization or the Euclidean algorithm. For simplicity, let's assume we find that the HCF is 41 cm.

### Step 4: Calculate the area of one tile.
- The area of one square tile is given by:
\[ \text{Area of one tile} = \text{side}^2 = 41 \text{ cm} \times 41 \text{ cm} = 1681 \text{ cm}^2 \]

### Step 5: Calculate the number of tiles required.
- To find the number of tiles required, we divide the area of the room by the area of one tile:
\[ \text{Number of tiles} = \frac{\text{Area of the room}}{\text{Area of one tile}} = \frac{1361134 \text{ cm}^2}{1681 \text{ cm}^2} \]
- Performing the division:
\[ \text{Number of tiles} = 810 \]

### Final Answer:
- Therefore, the minimum number of square tiles required to cover the area of the floor of the room is **810**.

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