Final answer:
The difference between the lengths of the two diagonals is 15 cm.
Step-by-step explanation:
To find the difference between the lengths of the two diagonals, we subtract the length of the smaller diagonal from the length of the larger diagonal.
The diagonal of the larger square is 27 cm, and the diagonal of the smaller square is 12 cm. So, the difference between the lengths of these two diagonals is:
27 cm - 12 cm = 15 cm
Therefore, the difference between the lengths of the two diagonals is 15 cm.