The length and broadth of room are 1075 cm and 825 cm, respectively. The floor is to be paved with square tiles of the largest possible size. The size of each tile is .

Options

A. `25 cm xx25 cm`
B. `50 cm xx 50 cm`
C. `20 cm xx20 cm`
D. `30 cm xx 30 cm`

Answer

To find the size of the largest possible square tiles that can be used to pave the floor of the room, we need to determine the greatest common divisor (GCD) of the room's length and breadth. Here are the steps to solve the problem:

### Step 1: Identify the dimensions of the room
The length of the room is 1075 cm and the breadth is 825 cm.

### Step 2: Find the GCD of the dimensions
To find the largest size of the square tile, we need to calculate the GCD of 1075 and 825.

**Using the Euclidean algorithm:**
1. Divide 1075 by 825 and find the remainder.
- \( 1075 \div 825 = 1 \) (quotient)
- Remainder: \( 1075 - 825 \times 1 = 250 \)

2. Now, apply the algorithm again using 825 and the remainder 250.
- \( 825 \div 250 = 3 \) (quotient)
- Remainder: \( 825 - 250 \times 3 = 75 \)

3. Next, apply the algorithm using 250 and the remainder 75.
- \( 250 \div 75 = 3 \) (quotient)
- Remainder: \( 250 - 75 \times 3 = 25 \)

4. Finally, apply the algorithm using 75 and the remainder 25.
- \( 75 \div 25 = 3 \) (quotient)
- Remainder: \( 75 - 25 \times 3 = 0 \)

Since the remainder is now 0, the last non-zero remainder is the GCD. Thus, GCD(1075, 825) = 25.

### Step 3: Determine the size of each tile
The size of each square tile that can be used to pave the floor is 25 cm x 25 cm.

### Final Answer
The size of each tile is **25 cm**.

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