I have tied my square bathroom wall with congruent square tiles. All the tiles are red, except those along the two diagonals, which are all blue. If `I` used `121` blue tiles, then the number of red tiles `I` used are

Options

A. `900`
B. `1800`
C. `3600`
D. `7200`

Explanation

To solve the problem, we need to determine the number of red tiles used in the square bathroom wall after knowing the number of blue tiles.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We have a square bathroom wall tiled with congruent square tiles.
- All tiles are red except those along the two diagonals, which are blue.
- We know that there are 121 blue tiles.

2. **Identifying the Size of the Square**:
- Let the side length of the square be \( n \). Therefore, the total number of tiles is \( n \times n = n^2 \).

3. **Finding the Number of Blue Tiles**:
- If \( n \) is odd, the formula for the number of blue tiles (which are along the diagonals) is given by:
\[ \text{Number of blue tiles} = 2n - 1 \]
- According to the problem, this equals 121:
\[ 2n - 1 = 121 \]

4. **Solving for \( n \)**:
- Rearranging the equation:
\[ 2n = 121 + 1 \]
\[ 2n = 122 \]
\[ n = \frac{122}{2} = 61 \]

5. **Calculating Total Number of Tiles**:
- Now that we have \( n = 61 \), we can find the total number of tiles:
\[ \text{Total tiles} = n^2 = 61 \times 61 = 3721 \]

6. **Calculating the Number of Red Tiles**:
- The number of red tiles can be found by subtracting the number of blue tiles from the total number of tiles:
\[ \text{Number of red tiles} = \text{Total tiles} - \text{Blue tiles} \]
\[ \text{Number of red tiles} = 3721 - 121 = 3600 \]

### Final Answer:
The number of red tiles used is **3600**.

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