To find the difference in the lengths of the diagonals of the two tiles, simply subtract the smaller diagonal from the larger diagonal.
The diagonals are:
- First tile: \( \sqrt{92} \) cm
- Second tile: \( \sqrt{82} \) cm
The difference can be calculated as follows:
\[ \sqrt{92} - \sqrt{82} \]
To compute this value, you can first find a numerical approximation of each square root:
- \( \sqrt{92} \approx 9.591 \)
- \( \sqrt{82} \approx 9.055 \)
Now, subtract the two values:
\[ 9.591 - 9.055 \approx 0.536 \]
Thus, the difference in the length of the diagonals is approximately 0.536 cm.
If you need the answer in its exact form, it remains \( \sqrt{92} - \sqrt{82} \) without further simplification unless you need a numerical approximation.