To find the perimeter of the dog pen, we need to add up the lengths of all the sides. The perimeter can be calculated using the formula:
Perimeter = 2m + 2n
1) m = 3 feet, n = 2 feet:
Perimeter = 2(3) + 2(2) = 6 + 4 = 10 feet
2) m = 5.5 feet, n = 3 feet:
Perimeter = 2(5.5) + 2(3) = 11 + 6 = 17 feet
3) m = 7.5 feet, n = 5.5 feet:
Perimeter = 2(7.5) + 2(5.5) = 15 + 11 = 26 feet
To determine if we can create a dog pen with these dimensions, we need to know the length of the available fencing material. If the perimeter of the dog pen is smaller or equal to the length of the fencing material, then we can create the dog pen. Otherwise, we cannot.
List of possible dimensions:
- For m = 3 feet and n = 2 feet, we can create a dog pen with a perimeter of 10 feet.
- For m = 5.5 feet and n = 3 feet, we can create a dog pen with a perimeter of 17 feet.
- For m = 7.5 feet and n = 5.5 feet, we can create a dog pen with a perimeter of 26 feet.
The dimensions that we should use to make the dog pen depend on the length of the available fencing material. If the available fencing material is longer than the largest perimeter (26 feet in this case), then we can create a dog pen using the dimensions m = 7.5 feet and n = 5.5 feet. If the available fencing material is shorter than 26 feet, we would need to choose a smaller set of dimensions.
Find the perimeter of the dog pen in terms of m and n . Will you be able to create a dog pen with the following dimensions? Explain your answers. m=3 feet by n=2 feet m=5.5 feet by n=3 feet m=7.5 feet by n=5.5 feet List the possible dimensions of the dog pen that you can make out of the available fencing material. Among the dimensions you listed, which should you use to make the dog pen? Explain your reasoning.
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