You have 20 feet of fencing material to make a pen for your dog. The design of the pen is given as follows.
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.
The perimeter of a rectangular pen can be found by adding up the lengths of all four sides.
For the dimensions m=3 feet by n=2 feet:
Perimeter = 2m + 2n = 2(3) + 2(2) = 6 + 4 = 10 feet
This pen can be made with 10 feet of fencing material, so it is possible to create this pen.
For the dimensions m=5.5 feet by n=3 feet:
Perimeter = 2m + 2n = 2(5.5) + 2(3) = 11 + 6 = 17 feet
This pen cannot be made with 20 feet of fencing material, so it is not possible to create this pen.
For the dimensions m=7.5 feet by n=5.5 feet:
Perimeter = 2m + 2n = 2(7.5) + 2(5.5) = 15 + 11 = 26 feet
This pen cannot be made with 20 feet of fencing material, so it is not possible to create this pen.
List of possible dimensions of the dog pen that can be made out of 20 feet of fencing material:
- m=3 feet, n=2 feet (perimeter = 10 feet)
- m=2 feet, n=3 feet (perimeter = 10 feet)
Out of these possible dimensions, it would be most reasonable to make the pen with the dimensions m=3 feet and n=2 feet. This is because it has the largest area (6 square feet) compared to the pen with dimensions m=2 feet and n=3 feet (which has an area of 6 square feet as well), making it more comfortable for the dog.