1. **State the problem:** We need to find the perimeter of a sector of a circle where the arc length is 21 cm and the central angle is 120 degrees. 2. **Recall the formula for the perimeter of a sector:** The perimeter $P$ of a sector is given by the sum of the arc length and the lengths of the two radii: $$P = 2r + s$$ where $r$ is the radius and $s$ is the arc length. 3. **Find the radius using the arc length formula:** The arc length $s$ is related to the radius $r$ and the central angle $\theta$ (in degrees) by: $$s = \frac{\theta}{360} \times 2\pi r$$ Rearranging to solve for $r$: $$r = \frac{s \times 360}{2\pi \theta}$$ 4. **Substitute the known values:** $$r = \frac{21 \times 360}{2\pi \times 120} = \frac{21 \times 3}{2\pi} = \frac{63}{2\pi}$$ 5. **Calculate the perimeter:** $$P = 2r + s = 2 \times \frac{63}{2\pi} + 21 = \frac{63}{\pi} + 21$$ 6. **Approximate the numerical value:** Using $\pi \approx 3.1416$, $$P \approx \frac{63}{3.1416} + 21 \approx 20.05 + 21 = 41.05$$ cm **Final answer:** The perimeter of the sector is approximately **41.05 cm**.