You have 20 feet of fencing material to make a pen for your dog. The design of the pen is given as follows.
An illustration shows a rectangle named as Dog Pen with length as lower m and width as lower n.
1:Find the perimeter of the dog pen in terms of m
and n
.
2: 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
3: List the possible dimensions of the dog pen that you can make out of the available fencing material.
4: Among the dimensions you listed, which should you use to make the dog pen? Explain your reasoning.
anonymous
asked
anonymously
1: The perimeter of the dog pen can be found by adding up the lengths of all four sides. The length is given as m and the width is given as n, so the perimeter is given by 2m + 2n.
2: For the dimensions m=3 feet, n=2 feet:
Perimeter = 2(3) + 2(2) = 6 + 4 = 10 feet
Since we have 20 feet of fencing material, this is possible.
For the dimensions m=5.5 feet, n=3 feet:
Perimeter = 2(5.5) + 2(3) = 11 + 6 = 17 feet
Since we only have 20 feet of fencing material, this is possible.
For the dimensions m=7.5 feet, n=5.5 feet:
Perimeter = 2(7.5) + 2(5.5) = 15 + 11 = 26 feet
Since we only have 20 feet of fencing material, this is not possible.
3: To find the possible dimensions of the dog pen, we need to consider the total length of the fencing material. We have 20 feet, so the perimeter of the dog pen should be less than or equal to 20 feet.
One way to list the possible dimensions is to consider the length and width as whole numbers and see what combinations give us a perimeter of 20 feet or less. Some possible dimensions that satisfy this constraint are:
m=4 feet, n=6 feet
m=2 feet, n=8 feet
m=5 feet, n=5 feet
4: Among the dimensions listed, we should use the dimensions m = 4 feet, n = 6 feet to make the dog pen. This is because the perimeter for this dimension is 2(4) + 2(6) = 16 feet, which is the largest possible perimeter that can be achieved with the given fencing material of 20 feet.