Select the correct answer.
The dimensions and number of animals are given for different corrals.
| Corral | Length | Width | Number of Animals |
| :----- | :---------- | :---------- | :---------------- |
| 1 | 50 meters | 40 meters | 110 |
| 2 | 60 meters | 35 meters | 115 |
| 3 | 55 meters | 45 meters | 125 |
| 4 | 65 meters | 40 meters | 130 |
The population constraints state that each corral should have at least 20 square meters for each animal. Which corral meets this requirement?
A. Corral 1
B. Corral 2
C. Corral 3
D. Corral 4
Answer (2)
Calculate the area of each corral using the formula A re a = L e n g t h × Wi d t h .
Determine the area per animal for each corral by dividing the total area by the number of animals.
Compare the area per animal to the minimum requirement of 20 square meters.
Identify that only Corral 4 meets the requirement with exactly 20 square meters per animal. Therefore, the answer is D .
Explanation
Calculate the area of each corral First, we need to calculate the area of each corral. The area of a rectangle is given by the formula: A re a = L e n g t h × Wi d t h For Corral 1: A re a 1 = 50 m e t ers × 40 m e t ers = 2000 s q u a re m e t ers For Corral 2: A re a 2 = 60 m e t ers × 35 m e t ers = 2100 s q u a re m e t ers For Corral 3: A re a 3 = 55 m e t ers × 45 m e t ers = 2475 s q u a re m e t ers For Corral 4: A re a 4 = 65 m e t ers × 40 m e t ers = 2600 s q u a re m e t ers
Calculate the area per animal for each corral Next, we need to calculate the area per animal for each corral. This is found by dividing the total area of the corral by the number of animals in it: A re a p er A nima l = N u mb er o f A nima l s T o t a l A re a For Corral 1: A re a p er A nima l 1 = 110 anima l s 2000 s q u a re m e t ers = 18.18 s q u a re m e t ers / anima l For Corral 2: A re a p er A nima l 2 = 115 anima l s 2100 s q u a re m e t ers = 18.26 s q u a re m e t ers / anima l For Corral 3: A re a p er A nima l 3 = 125 anima l s 2475 s q u a re m e t ers = 19.8 s q u a re m e t ers / anima l For Corral 4: A re a p er A nima l 4 = 130 anima l s 2600 s q u a re m e t ers = 20.0 s q u a re m e t ers / anima l
Compare with the minimum requirement Now, we compare the area per animal for each corral to the requirement that each animal should have at least 20 square meters.
Corral 1: 18.18 square meters/animal (Does not meet the requirement)
Corral 2: 18.26 square meters/animal (Does not meet the requirement)
Corral 3: 19.8 square meters/animal (Does not meet the requirement)
Corral 4: 20.0 square meters/animal (Meets the requirement)
Final Answer Only Corral 4 meets the requirement of at least 20 square meters per animal. Therefore, the correct answer is Corral 4.
Examples
Understanding area calculations is crucial in many real-world scenarios. For instance, when planning a garden, you need to calculate the area to determine how much soil to buy or how many plants you can fit. Similarly, in construction, calculating the area of a room helps determine the amount of flooring needed. These calculations ensure efficient use of resources and prevent overspending or shortages. Knowing how to calculate area helps in everyday tasks like home improvement projects or even planning events in a specific space.
Corral 4 is the only corral that meets the requirement of at least 20 square meters per animal with exactly 20.00 square meters per animal. Therefore, the correct answer is D.
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