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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

1 answer

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.