Question

Question 4

A'Leila is building a pen for her pet donkey. The pen is a rectangle with one side measuring b yards and the adjacent side measuring a yards.





4a. Which formulas could A'Leila use to calculate the perimeter of the donkey's pen? Be sure to select ALL that would work to calculate the perimeter.

(2 points)
Responses

a + a + b + b
a + a + b + b

2a + 2b
2 a + 2 b

a x b
a x b

a + 2b
a + 2 b
Question 2






4b. A'Leila knows that a = (12)
b. If side b of her donkey's pen is going to be 12 meters, how long should side a be using this equation?

(1 point)
Responses

6 meters
6 meters

12 meters
12 meters

24 meters
24 meters

12 12
meters
12 1 half meters
Question 3






4c. Using the dimensions from part b of this question, calculate the perimeter of the donkey's pen.

(2 points)
Responses

72 meters
72 meters

49 meters
49 meters

48 meters
48 meters

36 meters
36 meters
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Answer 1

### 4a. Which formulas could A'Leila use to calculate the perimeter of the donkey's pen?

The perimeter \( P \) of a rectangle is calculated using the formula:
\[
P = 2a + 2b
\]
or equivalently:
\[
P = a + a + b + b
\]

Therefore, the correct choices are:
- **a + a + b + b**
- **2a + 2b**

The other options:
- **a x b** (this calculates the area, not the perimeter)
- **a + 2b** (this does not correctly represent the perimeter of a rectangle)

### 4b. If side b of her donkey's pen is going to be 12 meters, how long should side a be using this equation?

Given that \( b = 12 \) meters, there is no additional equation provided in the question to determine \( a \). If we assume \( a \) is simply a variable that can take any value, it could be any positive measurement.

Therefore, the most reasonable response among the options provided must align with a potential context that may not have been included in the original question (additional specification).

If we assume that there is a characteristic ratio or relationship specified elsewhere (like \( a = b/2 \)), then the answer would relate to that.

If no context is provided, we cannot determine \( a \) specifically from the given options.

### 4c. Using the dimensions from part b of this question, calculate the perimeter of the donkey's pen.

If we assume from the context that \( a \) has been previously determined to be a certain value, we can still calculate the perimeter using the dimensions given (let’s assume A'Leila set \( a = 6 \) meters for our calculations).

If:
- \( a = 12 \) meters
- \( b = 12 \) meters

The perimeter \( P \) calculates as follows:
\[
P = 2a + 2b = 2(12) + 2(12) = 24 + 24 = 48 \text{ meters}
\]

Thus, the correct response is:
- **48 meters**

If \( a \) was to be something else, you would input that to the same formula to reach the perimeter accordingly.

Please clarify any additional details for more specific solutions.