1. The problem states that a semi-circle has a perimeter of 100 m and asks to find the length of the diameter in cm. 2. The perimeter $P$ of a semi-circle consists of the diameter plus half the circumference of a full circle: $$P = d + \pi r$$ where $d$ is the diameter and $r$ is the radius. 3. Since the diameter $d = 2r$, rewrite the perimeter formula as: $$P = d + \frac{\pi d}{2} = d\left(1 + \frac{\pi}{2}\right)$$ 4. Substitute $P = 100$ m: $$100 = d\left(1 + \frac{\pi}{2}\right)$$ 5. Solve for $d$: $$d = \frac{100}{1 + \frac{\pi}{2}} = \frac{100}{\frac{2 + \pi}{2}} = \frac{100 \times 2}{2 + \pi} = \frac{200}{2 + \pi}$$ 6. Approximate the value: $$d \approx \frac{200}{2 + 3.1416} = \frac{200}{5.1416} \approx 38.89\text{ meters}$$ 7. Convert diameter from meters to centimeters (1 m = 100 cm): $$d = 38.89 \times 100 = 3889\text{ cm}$$ 8. Final answer: The length of the diameter is approximately 3889 cm.