A `7xx24` rectangular thin wall has a `2xx2` square shaped window in such a way that the intersection of diagonals of rectangle and the intersection of diagonals of square coincide with each other. Which one of the following is correct?

Options

A. Diagonals of rectangle and that of square will be the same.
B. The diagonals of wall will intersect the vertical sides of the window.
C. The diagonals of wall will intersect the horizontal sides of the window.
D. none of the above

Answer

To solve the problem, we need to analyze the given rectangular wall and the square window, and determine the relationship between their diagonals.

### Step-by-Step Solution:

1. **Identify the Dimensions**:
- The dimensions of the rectangular wall are given as 7 units (height) and 24 units (width).
- The dimensions of the square window are given as 2 units by 2 units.

2. **Draw the Rectangle and Square**:
- Draw a rectangle with height 7 and width 24.
- Inside this rectangle, draw a square with each side measuring 2 units.

3. **Locate the Center Points**:
- The center of the rectangle can be found at the intersection of its diagonals. This point is located at:
\[ \left(\frac{24}{2}, \frac{7}{2}\right) = (12, 3.5) \]
- The center of the square is also at the intersection of its diagonals, which is at:
\[ \left(\frac{2}{2}, \frac{2}{2}\right) = (1, 1) \]
- However, since the problem states that the diagonals coincide, we need to position the square such that its center aligns with the rectangle's center.

4. **Positioning the Square**:
- To ensure that the diagonals of the square and rectangle coincide, the square must be positioned such that its center is at (12, 3.5).
- This means the square will be placed in a way that it is centered at this point.

5. **Analyze the Options**:
- **Option 1**: The diagonals of the rectangle and that of the square will be the same. This is incorrect because the lengths of the diagonals are different.
- **Option 2**: The diagonals of the wall will intersect the vertical sides of the window. This is correct since the diagonals of the rectangle will intersect the vertical sides of the square window.
- **Option 3**: The diagonals of the wall will intersect the horizontal sides of the window. This is incorrect as the diagonals of the rectangle do not intersect the horizontal sides of the square window.
- **Option 4**: None of the above. This is incorrect since we have found a correct option.

6. **Conclusion**:
- The correct answer is **Option 2**: The diagonals of the wall will intersect the vertical sides of the window.