Question

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)
(
1
2
)
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
1
2
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

Answer 1

To address your questions, I'll break down each part and provide the appropriate formulas and calculations.

### Question 1: Formulas for Calculating the Perimeter

To calculate the perimeter of a rectangle (which we will assume is the shape of the donkey's pen), the formulas that are applicable include:

1. **a + a + b + b** (This represents the addition of all four sides: two sides of length \( a \) and two sides of length \( b \)).
2. **2a + 2b** (This is a more concise way to represent the same calculation, using the perimeter formula \( P = 2(l + w) \) where \( l \) is length and \( w \) is width).

The formulas that do **not** calculate the perimeter are:
- **a x b** (This calculates the area, not the perimeter).
- **a + 2b** (This only accounts for one side \( a \) and two sides \( b \), not all four sides).

### Responses for Question 1:
- **a + a + b + b**
- **2a + 2b**

### Question 2: Length of side a

A'Leila has the equation:
- \( a = \left(12\right)\left(\frac{1}{2}\right)b \)

Given that side \( b \) is 12 meters, we can substitute \( b \) into the equation:

\[
a = 12 \times \frac{1}{2} \times 12
\]
\[
a = 12 \times 6
\]
\[
a = 72
\]

It appears I've simplified incorrectly. If the equation actually means \( a = \frac{1}{2}b \), we should do:

\[
a = \frac{1}{2} \times 12 = 6 \text{ meters}
\]

### Responses for Question 2:
- **6 meters**

### Question 3: Calculate the Perimeter

From question 2, we have:
- \( a = 6 \) meters
- \( b = 12 \) meters

Now we can calculate the perimeter using the formula \( P = 2a + 2b \):

\[
P = 2(6) + 2(12)
\]
\[
P = 12 + 24
\]
\[
P = 36 \text{ meters}
\]

The responses given don't include an option of 36 meters, so double-check the dimensions again.

However, using the original values without deriving incorrectly:
If they said all sides still were:
- \( a = 6 \) and \( b = 12 \) squeezed in per unit of total area instead of segments, then we still compute \( P \) as is.

### Final Responses:
- **Question 1:** a + a + b + b, 2a + 2b
- **Question 2:** 6 meters
- **Question 3:** No suitable options provided; valid P would be 36 meters, but the listed options didn't quantify that on review.