Final answer:
The perimeter of a sector with a central angle of 120 degrees and a radius of 5 cm is approximately 17.85 cm when rounded to the nearest tenth.
Step-by-step explanation:
To find the perimeter of a sector of a circle, we need to calculate the length of the arc of the sector and then add it to twice the radius, since the perimeter includes the arc and the two radii of the sector. The formula to find the length of an arc (L) with a central angle (θ, in degrees) and radius (r) is L = (θ/360) × 2πr. For a central angle of 120 degrees and a radius of 5 cm, the arc length L would be (120/360) × 2π × 5 = ½ × π × 5 ≈ 7.85 cm (rounded to the nearest tenth). Adding this arc length to twice the radius (2 × 5 = 10 cm) gives us the total perimeter of the sector: 7.85 cm + 10 cm = 17.85 cm, rounded to the nearest tenth.