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. 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.

Question

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. 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.

Answer 1

According to the given design, the dog pen consists of 4 sides, with two sides having length m and the other two sides having length n. Since all sides are connected, the perimeter of the dog pen is given by 2m + 2n.

Let's calculate the perimeter for each given set of dimensions:

1. m = 3 feet, n = 2 feet:
Perimeter = 2(3) + 2(2) = 6 + 4 = 10 feet.

2. m = 5.5 feet, n = 3 feet:
Perimeter = 2(5.5) + 2(3) = 11 + 6 = 17 feet.

3. m = 7.5 feet, n = 5.5 feet:
Perimeter = 2(7.5) + 2(5.5) = 15 + 11 = 26 feet.

Since we have 20 feet of fencing material, the dimensions (m and n) must satisfy the condition 2m + 2n ≤ 20.

Let's find the dimensions that satisfy this condition:

For m = 3 feet and n = 2 feet:
2(3) + 2(2) = 6 + 4 = 10 feet ≤ 20 feet (satisfies the condition).

For m = 5.5 feet and n = 3 feet:
2(5.5) + 2(3) = 11 + 6 = 17 feet ≤ 20 feet (satisfies the condition).

For m = 7.5 feet and n = 5.5 feet:
2(7.5) + 2(5.5) = 15 + 11 = 26 feet > 20 feet (does not satisfy the condition).

Therefore, we can create a dog pen with dimensions m = 3 feet and n = 2 feet or m = 5.5 feet and n = 3 feet.

Among these options, it is generally better to choose a larger pen size, so we should use m = 5.5 feet and n = 3 feet dimensions to make the dog pen.

Answer 2

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Answer 3

Sure! You only have 20 feet of fence to make a dog pen. The pen has two sides that are m feet long and two sides that are n feet long. The perimeter (the distance around the pen) is 2m + 2n.

Let's see if we can make a dog pen with these dimensions:

1. m = 3 feet, n = 2 feet:
Perimeter = 2(3) + 2(2) = 6 + 4 = 10 feet. Yes, you can make a dog pen with these dimensions!

2. m = 5.5 feet, n = 3 feet:
Perimeter = 2(5.5) + 2(3) = 11 + 6 = 17 feet. Yes, you can make a dog pen with these dimensions too!

3. m = 7.5 feet, n = 5.5 feet:
Perimeter = 2(7.5) + 2(5.5) = 15 + 11 = 26 feet. No, you can't make a dog pen with these dimensions because it's too big for the fence you have.

Out of the options, you can choose to make a dog pen with dimensions m = 3 feet and n = 2 feet, or m = 5.5 feet and n = 3 feet. It's generally better to have a bigger pen, so you should go with m = 5.5 feet and n = 3 feet.