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.
(3x2)x2=
(5.5x3)x2=
(7.5x5.5)x2=
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 all the sides of the pen.
For the pen with dimensions (3x2)x2:
The perimeter would be 2(3x2) + 2(2x2) = 6x + 4 + 4x + 4 = 10x + 8.
For the pen with dimensions (5.5x3)x2:
The perimeter would be 2(5.5x3) + 2(3x2) = 11x + 6 + 6x + 4 = 17x + 10.
For the pen with dimensions (7.5x5.5)x2:
The perimeter would be 2(7.5x5.5) + 2(5.5x3) = 15x + 11 + 11x + 6 = 26x + 17.
To determine if we can create a dog pen with the given dimensions, we need to compare the perimeters of each design to the available fencing material, which is 20 feet.
For the first design, 10x + 8 = 20.
Simplifying the equation, we have 10x = 12. Dividing both sides by 10, we get x = 1.2.
So, the first design can be created.
For the second design, 17x + 10 = 20.
Simplifying the equation, we have 17x = 10. Dividing both sides by 17, we get x ≈ 0.588.
So, the second design cannot be created as the value of x is not feasible for making a dog pen.
For the third design, 26x + 17 = 20.
Simplifying the equation, we have 26x = 3. Dividing both sides by 26, we get x ≈ 0.115.
So, the third design cannot be created as the value of x is not feasible for making a dog pen.
Possible dimensions that can be created out of the available fencing material would include any values of x that satisfy their respective perimeter equations:
For the first design, any value of x greater than or equal to 1.2 will work.
For the second design, no values of x will work as 0.588 is not feasible.
For the third design, no values of x will work as 0.115 is not feasible.
From the possible dimensions listed, we should use the first design with dimensions (3x2)x2 to make the dog pen because it is the only one that can be created with the given fencing material.