Question 4

Question

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.

(a height and b length)


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 = (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 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
49 meters

48 meters
48 meters

36 meters
36 meters

Answer 1

Question 4

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)

The formulas for calculating the perimeter \( P \) of a rectangle with dimensions \( a \) and \( b \) are:

1. \( a + a + b + b \) (This simplifies to \( 2a + 2b \))
2. \( 2a + 2b \) (This is the standard formula for the perimeter)
3. \( a \times b \) (This is incorrect; it calculates the area, not the perimeter)
4. \( a + 2b \) (This is incorrect; it does not give the full perimeter of the rectangle)

Correct Responses:

• \( a + a + b + b \)
• \( 2a + 2b \)

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4b. A'Leila knows that \( a = \frac{1}{2} b \). 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)

Since \( b = 12 \):

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

Correct Response:

• 6 meters

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4c. Using the dimensions from part b of this question, calculate the perimeter of the donkey's pen. (2 points)

Using \( a = 6 \) meters and \( b = 12 \) meters, we can calculate the perimeter:

\[ P = 2a + 2b = 2 \times 6 + 2 \times 12 = 12 + 24 = 36 \text{ meters} \]

Correct Response:

• 36 meters