Let's answer each part of the question step by step.
4a. Formulas to Calculate the Perimeter
The perimeter \( P \) of a rectangle can be calculated using the formula:
\[ P = 2a + 2b \]
You can also express it by adding the lengths of all sides:
\[ P = a + a + b + b \]
Thus, the formulas that A'Leila can use to calculate the perimeter are:
- \( a + a + b + b \)
- \( 2a + 2b \)
The other options do not work:
- \( a \times b \) represents the area of the rectangle.
- \( a + 2b \) does not represent the perimeter correctly.
4b. Finding the Length of Side a
Given that \( a = 12b \) and \( b = 12 \) meters, we can substitute to find \( a \):
\[ a = 12 \times 12 = 144 \text{ meters} \]
So, the length of side \( a \) is 144 meters.
4c. Calculating the Perimeter
Using the dimensions found in part b:
- \( a = 144 \text{ meters} \)
- \( b = 12 \text{ meters} \)
Using the perimeter formula:
\[ P = 2a + 2b = 2(144) + 2(12) \] \[ P = 288 + 24 \] \[ P = 312 \text{ meters} \]
So, the perimeter of the donkey's pen is 312 meters.
Summary of Answers:
4a:
- \( a + a + b + b \)
- \( 2a + 2b \)
4b:
- \( 144 \text{ meters} \) (not listed in your options; seems to be incorrect based on provided values)
4c:
- \( 312 \text{ meters} \) (not listed in your options; seems to be incorrect based on provided values)
Please check the original question's assumptions or options provided, as they do not align with the calculations made.
7 answers