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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.
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.
To find the perimeter of the dog pen in terms of m and n, we need to add up the lengths of all four sides of the rectangle.
Perimeter = 2m + 2n
For m = 3 feet and n = 2 feet:
Perimeter = 2(3) + 2(2) = 6 + 4 = 10 feet
For m = 5.5 feet and n = 3 feet:
Perimeter = 2(5.5) + 2(3) = 11 + 6 = 17 feet
For m = 7.5 feet and 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 the given dimensions, we need to check if the perimeter is less than or equal to 20 feet.
For m = 3 feet and n = 2 feet, the perimeter is 10 feet which is less than 20 feet. So, we can create a dog pen with these dimensions.
For m = 5.5 feet and n = 3 feet, the perimeter is 17 feet which is also less than 20 feet. So, we can create a dog pen with these dimensions.
For m = 7.5 feet and n = 5.5 feet, the perimeter is 26 feet which is greater than 20 feet. So, we cannot create a dog pen with these dimensions.
Possible dimensions of the dog pen that can be made out of the available fencing material include:
- m = 3 feet and n = 2 feet
- m = 5.5 feet and n = 3 feet
From these dimensions, the one we should use to make the dog pen depends on the specific requirements. If we want a smaller pen, we can use m = 3 feet and n = 2 feet. If we want a larger pen, we can use m = 5.5 feet and n = 3 feet.