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.



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

Answer 1

To calculate the perimeter of a rectangle, the formula used is typically:

\[ \text{Perimeter} = 2 \times (\text{length} + \text{width}) = 2a + 2b \]

Based on this, the correct formulas from the options you provided for calculating the perimeter of A'Leila's donkey pen are:

1. \( 2a + 2b \)
2. \( a + a + b + b \) (which simplifies to \( 2a + 2b \))
3. \( a + 2b \) (though this formula doesn't calculate the full perimeter of the rectangle, but it could represent a side in a different context, it’s not correct for full perimeter computation)

The following options do not work for calculating the perimeter:

• \( a \times b \) is the formula for the area of the rectangle, not the perimeter.
• The two options with only the sum of sides do not represent valid expressions without a multiplication by 2.

Thus, the valid formulas for the perimeter are:

• \( 2a + 2b \)
• \( a + a + b + b \)