1. **Problem statement:** We are given a rectangle whose length is twice its width and its perimeter is 54 cm. We need to find the width. 2. **Assign variables:** Let the width be $w$ cm. Then the length is $2w$ cm. 3. **Formula for perimeter of a rectangle:** $$\text{Perimeter} = 2(\text{Length} + \text{Width})$$ 4. **Substitute values:** $$54 = 2(2w + w)$$ 5. **Simplify the equation:** $$54 = 2(3w)$$ $$54 = 6w$$ 6. **Solve for width:** $$w = \frac{54}{6} = 9$$ **Answer:** The width of the rectangle is $9$ cm.