Explanation:

- Let the shorter side of the rectangle be \( x \) cm.

- The longer side is then \( 2x \) cm since it is twice the shorter side.

- The formula for the perimeter of a rectangle is \( P = 2 \times (\text{length} + \text{width}) \).

- Substituting the given values, we have \( 2 \times (x + 2x) = 54 \).

- This simplifies to \( 2 \times 3x = 54 \).

- Further simplifying, we get \( 6x = 54 \).

- Solving for \( x \), we find \( x = 9 \).

- The longer side, therefore, is \( 2x = 18 \) cm.

So, based on the options provided:

- Option 1: 14 cm – Incorrect, as the longer side is not 14 cm.

- Option 2: 9 cm – Incorrect, as this represents the shorter side.

- Option 3: 27 cm – Incorrect, as this is not the calculated longer side.

- Option 4: 18 cm – Correct! This is the calculated length of the longer side.