I need to design a site plan for a wildlife centre. In order to save money, I must design the plan using the least amount of fencing possible. The plot of land is 80 m wide by 100 m long, and it must be fenced off. Each section for each animal must be fenced off. The building for the hospital will measure 10 m by 20 m, but a fence does not have to be built around it. Each section must have a gate built into the fencing. Each section needs to be accessible without going through another section. The wooded area set aside for the Bears must take up 1/4 of the land. The section for the goats must take up 10 percent of the land. The surface area of the section for the wolves must be 1500 m sq. The section for the deers must take 20 percent. I must use the least amount of fencing.
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To design a site plan for the wildlife centre using the least amount of fencing possible, you can follow the steps below:
1. Determine the total area of the land:
- The plot of land is 80 m wide by 100 m long.
- The total area is calculated by multiplying the width (80 m) by the length (100 m):
Total Area = Width × Length = 80 m × 100 m = 8000 m²
2. Calculate the area needed for each animal section based on the given percentages:
- The wooded area for the bears must take up 1/4th (25%) of the land:
Bears Area = Total Area × 1/4 = 8000 m² × 1/4 = 2000 m²
- The section for the goats must take up 10% of the land:
Goats Area = Total Area × 10/100 = 8000 m² × 10/100 = 800 m²
- The section for the wolves must have an area of 1500 m².
- The section for the deers must take up 20% of the land:
Deers Area = Total Area × 20/100 = 8000 m² × 20/100 = 1600 m²
3. Determine the dimensions of each animal section using the calculated areas:
- Since the proportion of each animal section is not specified, you will have some flexibility in determining their dimensions. However, you could aim for rectangular sections.
- Let's assume you assign the bears area a rectangular shape with dimensions 40 m by 50 m:
Bears Area = Length × Width = 40 m × 50 m = 2000 m²
- You can assign the goats area a rectangular shape with dimensions 20 m by 40 m:
Goats Area = Length × Width = 20 m × 40 m = 800 m²
- For the wolves area, since the size needs to be exactly 1500 m², you can assign a rectangular shape with approximate dimensions of 30 m by 50 m:
Wolves Area = Length × Width = 30 m × 50 m = 1500 m²
- You can assign the deers area a rectangular shape with dimensions 20 m by 80 m:
Deers Area = Length × Width = 20 m × 80 m = 1600 m²
4. Calculate the remaining area after assigning sections for animals:
- Remaining Area = Total Area - (Bears Area + Goats Area + Wolves Area + Deers Area)
- Remaining Area = 8000 m² - (2000 m² + 800 m² + 1500 m² + 1600 m²) = 1500 m²
5. Determine the dimensions for the remaining area (to be fenced off):
- Since the remaining area can be any shape, you can assign approximate dimensions to simplify calculations.
- Let's assume you assign a rectangular shape with dimensions 30 m by 50 m:
Remaining Area = Length × Width = 30 m × 50 m = 1500 m²
6. Calculate the total perimeter of the fencing required:
- Perimeter = Sum of all sides of each animal section + Sum of all sides of the remaining area
- Perimeter = (2 × Length + 2 × Width) for each animal section + (2 × Length + 2 × Width) for the remaining area
- The perimeter of each section is calculated as follows:
- Bears Section Perimeter = 2 × (Length + Width) = 2 × (40 m + 50 m) = 180 m
- Goats Section Perimeter = 2 × (Length + Width) = 2 × (20 m + 40 m) = 120 m
- Wolves Section Perimeter = 2 × (Length + Width) = 2 × (30 m + 50 m) = 160 m
- Deers Section Perimeter = 2 × (Length + Width) = 2 × (20 m + 80 m) = 200 m
- Remaining Area Perimeter = 2 × (Length + Width) = 2 × (30 m + 50 m) = 160 m
- Total Perimeter = Bears Section Perimeter + Goats Section Perimeter + Wolves Section Perimeter + Deers Section Perimeter + Remaining Area Perimeter
- Total Perimeter = 180 m + 120 m + 160 m + 200 m + 160 m = 820 m
Therefore, the total perimeter of fencing required for the wildlife centre, using the least amount of fencing possible, is 820 meters.