Explanation:

- We have two wires with lengths expressed in centimeters: 1054 cm (10 m 54 cm) and 1156 cm (11 m 56 cm).

- The goal is to cut both wires into pieces of the same length, x cm, where x is an integer.

- We need the greatest common divisor (GCD) of 1054 and 1156 to find the maximum length of each piece.

- 42 is the GCD of 1054 and 1156.

- Hence, the longest possible length for each piece is 42 cm.

- Option:1, 42

- Correct because 42 is indeed the GCD of the two lengths.

- Option:2, 56

- Incorrect because 56 does not divide both lengths exactly.

- Option:3, 34

- Incorrect because 34 does not divide both lengths exactly.

- Option:4, 28

- Incorrect because 28 does not divide both lengths exactly.