you have 20 feet of fencing material to make a pen for your dog The design of the pen is given as follows
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
To determine if you can create a pen with the given dimensions, you need to calculate the perimeter of each design and compare it to the amount of fencing material available (20 feet).
For the first design, m=3 feet by n=2 feet, the perimeter can be calculated as follows:
Perimeter = 2m + 2n = 2(3) + 2(2) = 6 + 4 = 10 feet
Since the perimeter of this pen is 10 feet and you have 20 feet of fencing material, you can create this pen design.
For the second design, m=5.5 feet by n=3 feet, the perimeter can be calculated as follows:
Perimeter = 2m + 2n = 2(5.5) + 2(3) = 11 + 6 = 17 feet
Since the perimeter of this pen is 17 feet and you only have 20 feet of fencing material, it is not possible to create this pen design.
For the third design, m=7.5 feet by n=5.5 feet, the perimeter can be calculated as follows:
Perimeter = 2m + 2n = 2(7.5) + 2(5.5) = 15 + 11 = 26 feet
Since the perimeter of this pen is 26 feet and you only have 20 feet of fencing material, it is not possible to create this pen design.
Therefore, you can create a pen with dimensions m=3 feet by n=2 feet, but not with dimensions m=5.5 feet by n=3 feet or m=7.5 feet by n=5.5 feet.