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.
a
M = 3 feet by n = 2 feet
b
M = 5.5 feet by n = 3 feet
c
M = 7.5 feet by n = 5.5 feet
To determine if you can create a dog pen with the given dimensions, we need to calculate the perimeter of each pen design and compare it to the available fencing material, which is 20 feet.
a) M = 3 feet by n = 2 feet
Perimeter = 2(M + n) = 2(3 + 2) = 2(5) = 10 feet
Since the perimeter is less than the available fencing material of 20 feet, it is possible to create a pen with these dimensions.
b) M = 5.5 feet by n = 3 feet
Perimeter = 2(M + n) = 2(5.5 + 3) = 2(8.5) = 17 feet
The perimeter is still less than the available fencing material of 20 feet, so it is possible to create a pen with these dimensions.
c) M = 7.5 feet by n = 5.5 feet
Perimeter = 2(M + n) = 2(7.5 + 5.5) = 2(13) = 26 feet
The perimeter is greater than the available fencing material of 20 feet, so it is not possible to create a pen with these dimensions.
Therefore, you will be able to create dog pens with dimensions (a) M = 3 feet by n = 2 feet and (b) M = 5.5 feet by n = 3 feet, while it is not possible to create a dog pen with dimensions (c) M = 7.5 feet by n = 5.5 feet.