To solve the questions step-by-step:
4a. Which formulas could A'Leila use to calculate the perimeter of the donkey's pen?
The formula for the perimeter \( P \) of a rectangle with length \( a \) and width \( b \) is given by: \[ P = 2a + 2b \] or \[ P = a + a + b + b \]
From the options provided:
- a + a + b + b
- 2a + 2b
Both of these are correct. The formulas related to area (like \( a \times b \)) or those involving only one dimension will not give the perimeter, so they are incorrect:
- a x b (not a perimeter formula)
- a + 2b (not a correct perimeter formula)
Correct responses:
- \( a + a + b + b \)
- \( 2a + 2b \)
4b. If side b of her donkey's pen is going to be 12 meters, what should side a be using the equation a = (12)?
It seems there’s a misunderstanding here in the question. If "a" is not specified and only \( b = 12 \) meters is given without an additional relationship to find \( a \), then we can’t determine \( a \) based on the information provided.
If the problem states that A'Leila has an equation where \( a \) somehow relates to \( b \), clarifying that equation is necessary to determine \( a \). However, if the equation or rule is simply \( a = b = 12 \), then:
- 12 meters could be one of the responses.
Based on the information provided these are not clear options, so it would be necessary to provide additional context.
4c. Using the dimensions from part b of this question, calculate the perimeter of the donkey's pen.
Assuming that \( b = 12 \) meters and if we previously assumed \( a = 12 \) meters or did not derive anything specific about \( a \), calculating the perimeter for both sides equal:
- Perimeter \( P = 2a + 2b = 2(12) + 2(12) = 24 + 24 = 48 \) meters.
If \( a = 6 \) (assuming half from b since 12 might have various interpretations):
- \( P = 2(6) + 2(12) = 12 + 24 = 36 \) meters.
From the options provided, if \( a \) was determined to be \( 12 \) as well: Correct response for \( P = 48 \) meters based on common dimensions for rectangle if both sides were stated as equal to 12.
Final Answers Recap:
- 4a: \( a + a + b + b \) and \( 2a + 2b \) are correct!
- 4b: Without a clear rule for \( a \), cannot conclusively say without further information, might deduce \( a = 12 \) meters.
- 4c: 48 meters based on \( 12 \) meters each for both sides.