Answer :
To determine which corral meets the population constraint of having at least 20 square meters for each animal, let's analyze each corral step-by-step.
We are given the following dimension and animal data:
- Corral 1: Length = 50 meters, Width = 40 meters, Number of Animals = 110
- Corral 2: Length = 60 meters, Width = 35 meters, Number of Animals = 115
- Corral 3: Length = 55 meters, Width = 45 meters, Number of Animals = 125
- Corral 4: Length = 65 meters, Width = 40 meters, Number of Animals = 130
To verify whether a corral meets the requirement, we need to calculate the area of each corral and then determine the area available per animal. Let's follow these steps for each corral:
### Corral 1:
1. Calculate the total area:
[tex]\[ \text{Area} = \text{Length} \times \text{Width} = 50 \times 40 = 2000 \text{ square meters} \][/tex]
2. Calculate the area per animal:
[tex]\[ \text{Area per animal} = \frac{\text{Total area}}{\text{Number of animals}} = \frac{2000}{110} \approx 18.18 \text{ square meters/animal} \][/tex]
This value is less than 20 square meters, so Corral 1 does not meet the requirement.
### Corral 2:
1. Calculate the total area:
[tex]\[ \text{Area} = \text{Length} \times \text{Width} = 60 \times 35 = 2100 \text{ square meters} \][/tex]
2. Calculate the area per animal:
[tex]\[ \text{Area per animal} = \frac{\text{Total area}}{\text{Number of animals}} = \frac{2100}{115} \approx 18.26 \text{ square meters/animal} \][/tex]
This value is also less than 20 square meters, so Corral 2 does not meet the requirement.
### Corral 3:
1. Calculate the total area:
[tex]\[ \text{Area} = \text{Length} \times \text{Width} = 55 \times 45 = 2475 \text{ square meters} \][/tex]
2. Calculate the area per animal:
[tex]\[ \text{Area per animal} = \frac{\text{Total area}}{\text{Number of animals}} = \frac{2475}{125} = 19.8 \text{ square meters/animal} \][/tex]
This value is still less than 20 square meters, so Corral 3 does not meet the requirement.
### Corral 4:
1. Calculate the total area:
[tex]\[ \text{Area} = \text{Length} \times \text{Width} = 65 \times 40 = 2600 \text{ square meters} \][/tex]
2. Calculate the area per animal:
[tex]\[ \text{Area per animal} = \frac{\text{Total area}}{\text{Number of animals}} = \frac{2600}{130} = 20 \text{ square meters/animal} \][/tex]
This value is exactly 20 square meters, so Corral 4 meets the requirement.
Therefore, the corral that meets the population constraint of having at least 20 square meters per animal is:
Corral 4
So the correct answer is D. Corral 4.
We are given the following dimension and animal data:
- Corral 1: Length = 50 meters, Width = 40 meters, Number of Animals = 110
- Corral 2: Length = 60 meters, Width = 35 meters, Number of Animals = 115
- Corral 3: Length = 55 meters, Width = 45 meters, Number of Animals = 125
- Corral 4: Length = 65 meters, Width = 40 meters, Number of Animals = 130
To verify whether a corral meets the requirement, we need to calculate the area of each corral and then determine the area available per animal. Let's follow these steps for each corral:
### Corral 1:
1. Calculate the total area:
[tex]\[ \text{Area} = \text{Length} \times \text{Width} = 50 \times 40 = 2000 \text{ square meters} \][/tex]
2. Calculate the area per animal:
[tex]\[ \text{Area per animal} = \frac{\text{Total area}}{\text{Number of animals}} = \frac{2000}{110} \approx 18.18 \text{ square meters/animal} \][/tex]
This value is less than 20 square meters, so Corral 1 does not meet the requirement.
### Corral 2:
1. Calculate the total area:
[tex]\[ \text{Area} = \text{Length} \times \text{Width} = 60 \times 35 = 2100 \text{ square meters} \][/tex]
2. Calculate the area per animal:
[tex]\[ \text{Area per animal} = \frac{\text{Total area}}{\text{Number of animals}} = \frac{2100}{115} \approx 18.26 \text{ square meters/animal} \][/tex]
This value is also less than 20 square meters, so Corral 2 does not meet the requirement.
### Corral 3:
1. Calculate the total area:
[tex]\[ \text{Area} = \text{Length} \times \text{Width} = 55 \times 45 = 2475 \text{ square meters} \][/tex]
2. Calculate the area per animal:
[tex]\[ \text{Area per animal} = \frac{\text{Total area}}{\text{Number of animals}} = \frac{2475}{125} = 19.8 \text{ square meters/animal} \][/tex]
This value is still less than 20 square meters, so Corral 3 does not meet the requirement.
### Corral 4:
1. Calculate the total area:
[tex]\[ \text{Area} = \text{Length} \times \text{Width} = 65 \times 40 = 2600 \text{ square meters} \][/tex]
2. Calculate the area per animal:
[tex]\[ \text{Area per animal} = \frac{\text{Total area}}{\text{Number of animals}} = \frac{2600}{130} = 20 \text{ square meters/animal} \][/tex]
This value is exactly 20 square meters, so Corral 4 meets the requirement.
Therefore, the corral that meets the population constraint of having at least 20 square meters per animal is:
Corral 4
So the correct answer is D. Corral 4.
