To determine which corral meets the requirement that each animal should have at least 20 square meters of space, we need to calculate the area available per animal in each corral and then check if this area meets or exceeds the constraint of 20 square meters per animal.
The area [tex]\( A \)[/tex] of a rectangular corral can be found using its length [tex]\( L \)[/tex] and width [tex]\( W \)[/tex]:
[tex]\[ A = L \times W \][/tex]
Then, the area per animal is:
[tex]\[ \text{Area per animal} = \frac{A}{\text{Number of Animals}} \][/tex]
Let's calculate this step by step for each corral:
1. Corral 1:
- Length [tex]\( L = 50 \)[/tex] meters
- Width [tex]\( W = 40 \)[/tex] meters
- Number of Animals = 110
- Total area [tex]\( A = 50 \times 40 = 2000 \)[/tex] square meters
- Area per animal [tex]\( \frac{2000}{110} \approx 18.18 \)[/tex] square meters
2. Corral 2:
- Length [tex]\( L = 60 \)[/tex] meters
- Width [tex]\( W = 35 \)[/tex] meters
- Number of Animals = 115
- Total area [tex]\( A = 60 \times 35 = 2100 \)[/tex] square meters
- Area per animal [tex]\( \frac{2100}{115} \approx 18.26 \)[/tex] square meters
3. Corral 3:
- Length [tex]\( L = 55 \)[/tex] meters
- Width [tex]\( W = 45 \)[/tex] meters
- Number of Animals = 125
- Total area [tex]\( A = 55 \times 45 = 2475 \)[/tex] square meters
- Area per animal [tex]\( \frac{2475}{125} = 19.8 \)[/tex] square meters
4. Corral 4:
- Length [tex]\( L = 65 \)[/tex] meters
- Width [tex]\( W = 40 \)[/tex] meters
- Number of Animals = 130
- Total area [tex]\( A = 65 \times 40 = 2600 \)[/tex] square meters
- Area per animal [tex]\( \frac{2600}{130} = 20 \)[/tex] square meters
Now, let's check which corrals meet the requirement of at least 20 square meters per animal:
- Corral 1: [tex]\( 18.18 \)[/tex] square meters (Does not meet the requirement)
- Corral 2: [tex]\( 18.26 \)[/tex] square meters (Does not meet the requirement)
- Corral 3: [tex]\( 19.8 \)[/tex] square meters (Does not meet the requirement)
- Corral 4: [tex]\( 20 \)[/tex] square meters (Meets the requirement)
Therefore, the corral that meets the requirement is:
D. Corral 4
