1. **State the problem:**
Kobe's walking path consists of two straight sides each 100 m long and two semicircular ends with a distance of 18 m between the sides.
2. **Formula for the perimeter of the path:**
The path is like a rectangle with semicircles at the ends. The total distance (perimeter) is the sum of the lengths of the two straight sides plus the circumference of the full circle formed by the two semicircles.
$$\text{Perimeter} = 2 \times \text{length of straight sides} + \text{circumference of full circle}$$
3. **Calculate the circumference of the full circle:**
The diameter of the semicircle is the distance between the sides, which is 18 m.
$$\text{Radius} = \frac{18}{2} = 9 \text{ m}$$
$$\text{Circumference} = 2 \pi r = 2 \pi \times 9 = 18 \pi$$
4. **Calculate the total distance for one lap:**
$$\text{Perimeter} = 2 \times 100 + 18 \pi = 200 + 18 \pi$$
5. **Evaluate the numerical value:**
$$200 + 18 \times 3.1416 = 200 + 56.5488 = 256.5488$$
Rounded to two decimal places:
$$256.55 \text{ metres}$$
6. **Find the number of complete laps to walk at least 5 km (5000 m):**
$$\text{Number of laps} = \left\lfloor \frac{5000}{256.55} \right\rfloor = \left\lfloor 19.49 \right\rfloor = 19$$
**Final answers:**
- Distance for one full lap: **256.55 metres**
- Number of complete laps needed for at least 5 km: **19 laps**
Puppy Walk Path Dd870F
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