To determine which corral meets the requirement of providing at least 20 square meters per animal, we need to perform the following steps for each corral:
1. Calculate the area of each corral.
2. Calculate the space per animal by dividing the area by the number of animals.
3. Compare the space per animal with the required 20 square meters.
Let's go through these steps for each corral:
### Corral 1:
- Length: 50 meters
- Width: 40 meters
- Number of Animals: 110
Area Calculation:
[tex]\[ \text{Area}_{1} = 50 \times 40 = 2000 \text{ square meters} \][/tex]
Space per Animal Calculation:
[tex]\[ \text{Space per animal}_{1} = \frac{2000}{110} \approx 18.18 \text{ square meters} \][/tex]
18.18 square meters per animal is less than 20 square meters, so Corral 1 does not meet the requirement.
### Corral 2:
- Length: 60 meters
- Width: 35 meters
- Number of Animals: 115
Area Calculation:
[tex]\[ \text{Area}_{2} = 60 \times 35 = 2100 \text{ square meters} \][/tex]
Space per Animal Calculation:
[tex]\[ \text{Space per animal}_{2} = \frac{2100}{115} \approx 18.26 \text{ square meters} \][/tex]
18.26 square meters per animal is also less than 20 square meters, so Corral 2 does not meet the requirement.
### Corral 3:
- Length: 55 meters
- Width: 45 meters
- Number of Animals: 125
Area Calculation:
[tex]\[ \text{Area}_{3} = 55 \times 45 = 2475 \text{ square meters} \][/tex]
Space per Animal Calculation:
[tex]\[ \text{Space per animal}_{3} = \frac{2475}{125} = 19.8 \text{ square meters} \][/tex]
19.8 square meters per animal is still less than 20 square meters, so Corral 3 does not meet the requirement.
### Corral 4:
- Length: 65 meters
- Width: 40 meters
- Number of Animals: 130
Area Calculation:
[tex]\[ \text{Area}_{4} = 65 \times 40 = 2600 \text{ square meters} \][/tex]
Space per Animal Calculation:
[tex]\[ \text{Space per animal}_{4} = \frac{2600}{130} = 20 \text{ square meters} \][/tex]
20 square meters per animal exactly meets the requirement, so Corral 4 does meet the requirement.
### Conclusion
The corral that meets the requirement is:
D. Corral 4
