To determine which corral meets the requirement of providing at least 20 square meters per animal, we follow these steps:
1. Calculate the area of each corral:
- Corral 1:
[tex]\( \text{Length} = 50 \, \text{meters}, \text{Width} = 40 \, \text{meters} \)[/tex]
[tex]\[ \text{Area} = 50 \times 40 = 2000 \, \text{square meters} \][/tex]
- Corral 2:
[tex]\( \text{Length} = 60 \, \text{meters}, \text{Width} = 35 \, \text{meters} \)[/tex]
[tex]\[ \text{Area} = 60 \times 35 = 2100 \, \text{square meters} \][/tex]
- Corral 3:
[tex]\( \text{Length} = 55 \, \text{meters}, \text{Width} = 45 \, \text{meters} \)[/tex]
[tex]\[ \text{Area} = 55 \times 45 = 2475 \, \text{square meters} \][/tex]
- Corral 4:
[tex]\( \text{Length} = 65 \, \text{meters}, \text{Width} = 40 \, \text{meters} \)[/tex]
[tex]\[ \text{Area} = 65 \times 40 = 2600 \, \text{square meters} \][/tex]
2. Calculate the required area for the animals in each corral:
- For each animal, 20 square meters are required. Thus, compute the required area based on the number of animals.
- Corral 1:
[tex]\( 110 \, \text{animals} \times 20 \, \text{square meters per animal} = 2200 \, \text{square meters} \)[/tex]
- Corral 2:
[tex]\( 115 \, \text{animals} \times 20 \, \text{square meters per animal} = 2300 \, \text{square meters} \)[/tex]
- Corral 3:
[tex]\( 125 \, \text{animals} \times 20 \, \text{square meters per animal} = 2500 \, \text{square meters} \)[/tex]
- Corral 4:
[tex]\( 130 \, \text{animals} \times 20 \, \text{square meters per animal} = 2600 \, \text{square meters} \)[/tex]
3. Compare the actual corral area with the required area:
- Corral 1: [tex]\( \text{Actual Area} = 2000 \, \text{square meters}, \text{Required Area} = 2200 \, \text{square meters} \)[/tex]
- [tex]\( 2000 < 2200 \)[/tex] (Does not meet the requirement)
- Corral 2: [tex]\( \text{Actual Area} = 2100 \, \text{square meters}, \text{Required Area} = 2300 \, \text{square meters} \)[/tex]
- [tex]\( 2100 < 2300 \)[/tex] (Does not meet the requirement)
- Corral 3: [tex]\( \text{Actual Area} = 2475 \, \text{square meters}, \text{Required Area} = 2500 \, \text{square meters} \)[/tex]
- [tex]\( 2475 < 2500 \)[/tex] (Does not meet the requirement)
- Corral 4: [tex]\( \text{Actual Area} = 2600 \, \text{square meters}, \text{Required Area} = 2600 \, \text{square meters} \)[/tex]
- [tex]\( 2600 \geq 2600 \)[/tex] (Meets the requirement)
4. Conclusion:
The only corral that meets the requirement of providing at least 20 square meters per animal is Corral 4.
Answer: D. Corral 4
