Question

Choose a value for a that is greater than 5 and less than 15. Evaluate the

perimeter of the pen for that value, using one of the expressions that you
wrote.
My expression: 2a +2b

Answer 1

[AI-generated answer — Bot GPT 3.5]

Since the problem only asks for a value for "a", we can choose "a" directly and then calculate the perimeter using the expression 2a + 2b.

Let's choose a = 8.

Using the expression 2a + 2b:
Perimeter = 2(8) + 2b
Perimeter = 16 + 2b

As we don't have any information about the value of b, we can't calculate the exact perimeter, but we can write it as a function of b:

Perimeter = 16 + 2b

So, for a = 8, the perimeter of the pen, using the given expression, is 16 + 2b.

Answer 2

. Explain why you used that expression to evaluate the perimeter of the

donkey’s pen.

Answer 3

[AI-generated answer — Bot GPT 3.5]

I used the expression 2a + 2b to evaluate the perimeter of the donkey's pen because it is a common formula for finding the perimeter of a rectangular shape.

In the given problem, we have the value for "a" but not for "b", so we need to keep both variables in the expression. The expression 2a + 2b represents the sum of the lengths of all four sides of the rectangular pen.

Since the donkey's pen is assumed to be rectangular, the perimeter can be calculated by adding the lengths of the two equal sides (represented by 2a) and the lengths of the other two equal sides (represented by 2b). This formula holds true for any rectangular shape.

Using this formula allows us to find the perimeter of the pen only with the given values for "a" and "b" or as a function of "b".

Answer 4

Try This

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.

Answer 5

[AI-generated answer — Bot GPT 3.5]

To find the perimeter of the dog pen in terms of m and n, we can use the formula for the perimeter of a rectangle, which is P = 2m + 2n.

Using the given dimensions, let's calculate the perimeters:

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

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

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

Now let's analyze if we can create a dog pen with these dimensions:

- m = 3 feet, n = 2 feet:
Since the perimeter is 10 feet and we have 20 feet of fencing material, it is possible to create a dog pen of these dimensions.

- m = 5.5 feet, n = 3 feet:
Since the perimeter is 17 feet and we have 20 feet of fencing material, it is possible to create a dog pen of these dimensions.

- m = 7.5 feet, n = 5.5 feet:
Since the perimeter is 26 feet and we have 20 feet of fencing material, it is not possible to create a dog pen of these dimensions. We do not have enough fencing material to enclose the entire pen.

Possible dimensions of the dog pen that can be created out of the available fencing material are:
- m = 3 feet, n = 2 feet
- m = 5.5 feet, n = 3 feet

Out of these dimensions, we should use m = 3 feet and n = 2 feet to make the dog pen because it is the only set of dimensions that allows us to use all the available 20 feet of fencing material to enclose the pen.