To solve the problem of how many posts and rails are needed for re-fencing the rectangular field, we need to consider the following from the image:

Key Dimensions:

• The field has dimensions of 64.8 meters by 63.6 meters.
• There are two gates, each 2.4 meters wide.
• The posts are placed 1.8 meters apart (center to center).
• Posts are also located at the edges of the gates.

Steps:

1. Total Perimeter of the Field:

The perimeter of the rectangular field is calculated as: $P = 2 \times (64.8 + 63.6) = 2 \times 128.4 = 256.8 \, \text{meters}$

2. Length of the Gates:

The total length occupied by the two gates is: $L_{\text{gates}} = 2 \times 2.4 = 4.8 \, \text{meters}$

3. Effective Length to Fence:

The total length that needs to be fenced (excluding the gates) is: $L_{\text{fence}} = P - L_{\text{gates}} = 256.8 - 4.8 = 252.0 \, \text{meters}$

4. Number of Posts Needed:

Since posts are placed every 1.8 meters, the number of posts required is: $N_{\text{posts}} = \frac{L_{\text{fence}}}{1.8} + 1 = \frac{252.0}{1.8} + 1 = 140 + 1 = 141 \, \text{posts}$ We add 1 because a post is needed at both ends of the fencing.

5. Number of Rails Needed:

Each section between posts requires 3 rails. Since there are 140 sections (141 posts means 140 gaps between them), the total number of rails needed is: $N_{\text{rails}} = 140 \times 3 = 420 \, \text{rails}$

Conclusion:

• Number of Posts: 141 posts
• Number of Rails: 420 rails

Would you like more details on any specific step or further clarifications?

Related Questions:

1. How do we account for irregular shapes in fencing calculations?
2. What happens if the posts are placed at a different interval (e.g., 2.0 meters)?
3. How would the calculations change if the gates were of different sizes?
4. How does terrain or slope affect the number of posts and rails required?
5. What is the standard thickness of the rails in a typical fencing setup?

Tip:

When calculating fencing materials, always remember to include the number of posts required for gate support, as these are not accounted for in regular perimeter calculations.