To find the difference in the lengths of the diagonals of the two tiles, we subtract the length of the second diagonal from the first diagonal. The diagonals are given as \( \sqrt{92} \) centimeters and \( \sqrt{82} \) centimeters.
The difference is calculated as follows:
\[ \text{Difference} = \sqrt{92} - \sqrt{82} \]
Now, we can calculate the numeric values of \( \sqrt{92} \) and \( \sqrt{82} \):
- \( \sqrt{92} \) is approximately \( 9.591663 \) (as \( 92 \) is between \( 81 \) and \( 100 \)).
- \( \sqrt{82} \) is approximately \( 9.055 \) (as \( 82 \) is between \( 81 \) and \( 100 \)).
Calculating the difference:
\[ \text{Difference} \approx 9.591663 - 9.055 = 0.536663 \]
So the difference in the diagonal lengths, rounded to two decimal places, is:
\[ \text{Difference} \approx 0.54 \text{ cm} \]
Thus, the difference in the length of the diagonals is approximately \( 0.54 \) centimeters.