Question

Choose a value for a that is greater than 5 and less than 15 ( use 10 ) . Evaluate the
perimeter of the pen for that value, using one of the expressions that you
wrote. (use a + b + a + b = 2a + 2b)

Answer 1

also here is the past question if it helps

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’Leila knows that a = 1/3b

Answer 2

get rid of the ( { [ so its easier for me to read

Answer 3

your using the " a+ b + a + b = 2a + 2b " right?

Answer 4

i dont get it

Answer 5

WITHOUT ( { [

Answer 6

To evaluate the perimeter of the pen using the expression \( P = 2a + 2b \), we need both the length \( a \) and the width \( b \) of the pen.

Given \( a = 10 \), we still need a value for \( b \). Let's choose a value for \( b \) that is also reasonable for a pen; for example, we can say \( b = 5 \).

Now, we can calculate the perimeter \( P \):

\[
P = 2a + 2b
\]

Substituting the values of \( a \) and \( b \):

\[
P = 2(10) + 2(5)
\]
\[
P = 20 + 10
\]
\[
P = 30
\]

Thus, the perimeter of the pen with \( a = 10 \) and \( b = 5 \) is \( 30 \) units.

Answer 7

Thanks for providing the additional context regarding the relationship between the sides of the rectangle. We know that:

- \( a = \frac{1}{3}b \)

To find the perimeter using this relationship, we can express the perimeter in terms of \( b \):

1. Start with the formula for perimeter:
\[
P = 2a + 2b
\]

2. Substitute \( a = \frac{1}{3}b \) into the perimeter formula:
\[
P = 2\left(\frac{1}{3}b\right) + 2b
\]

3. Simplify the equation:
\[
P = \frac{2}{3}b + 2b
\]
To add these, convert \( 2b \) into a fraction with a denominator of 3:
\[
P = \frac{2}{3}b + \frac{6}{3}b = \frac{8}{3}b
\]

Now, let's evaluate the perimeter using \( b \) when \( a = 10 \) yards. From the relationship \( a = \frac{1}{3}b \), we can find \( b \):

\[
10 = \frac{1}{3}b \implies b = 10 \times 3 = 30 \text{ yards}
\]

Now we calculate the perimeter \( P \) using \( b = 30 \):

\[
P = \frac{8}{3}(30)
\]
\[
P = \frac{240}{3} = 80 \text{ yards}
\]

Thus, the perimeter of the pen, given that \( a = 10 \) and using the relationship \( a = \frac{1}{3}b \), is **80 yards**.

Answer 8

Sure! Let’s rewrite the calculations without parentheses for better readability.

### Given:
- a = 1/3b

### Perimeter Formula:
The perimeter, P, of the rectangle can be expressed as:
P = 2a + 2b

### Substitute a in terms of b:
P = 2 * (1/3)b + 2b

### Simplifying the equation:
P = (2/3)b + 2b

Convert 2b to a fraction with a denominator of 3:
P = (2/3)b + (6/3)b

Now combine the fractions:
P = (8/3)b

### Now, find b when a = 10:
From the relationship a = 1/3b:
10 = (1/3)b

To find b, multiply both sides by 3:
b = 10 * 3
b = 30

### Calculate the perimeter using b = 30:
P = (8/3)(30)

Now simplify:
P = 240/3
P = 80

### Conclusion:
The perimeter of the pen is 80 yards.

Answer 9

Yes, that's correct! The formula \( P = a + b + a + b \) simplifies to \( P = 2a + 2b \), which is used to calculate the perimeter of a rectangle where \( a \) is one side and \( b \) is the adjacent side.

Let's clarify and follow this overall process step by step using the relationship \( a = \frac{1}{3}b \) and the perimeter calculation.

1. **Given the relationship:**
- \( a = \frac{1}{3}b \)

2. **Perimeter formula:**
Using the formula for perimeter:
\[
P = a + b + a + b = 2a + 2b
\]

3. **Substituting \( a \):**
Substitute \( a \) in terms of \( b \):
- Since \( a = \frac{1}{3}b \), we substitute \( a \) in the perimeter formula:
\[
P = 2\left(\frac{1}{3}b\right) + 2b
\]

4. **Simplifying the formula:**
\[
P = \frac{2}{3}b + 2b
\]
Now convert \( 2b \) to have a common denominator:
\[
P = \frac{2}{3}b + \frac{6}{3}b = \frac{8}{3}b
\]

5. **Finding \( b \):**
Determine \( b \) when \( a \) is given as 10:
- From \( a = \frac{1}{3}b \):
\[
10 = \frac{1}{3}b
\]
Multiply both sides by 3:
\[
b = 30
\]

6. **Calculating the perimeter:**
Now use \( b = 30 \) in the perimeter formula:
\[
P = \frac{8}{3}(30) = \frac{240}{3} = 80
\]

### Conclusion:
So using the relationship \( a + b + a + b = 2a + 2b \), the perimeter of the pen is **80 yards**.

Answer 10

Let’s break it down step by step in a clearer way, focusing on using the perimeter formula and the relationship between \( a \) and \( b \).

### 1. Understanding the Rectangle
- The rectangle has sides:
- Side \( a \) (length)
- Side \( b \) (width)

### 2. Relationship Between Sides
You mentioned that \( a \) is connected to \( b \) by the equation:
\[
a = \frac{1}{3}b
\]
This means that side \( a \) is one-third the length of side \( b \).

### 3. Perimeter Formula
The formula for the perimeter \( P \) of a rectangle is:
\[
P = a + b + a + b
\]
This can be simplified to:
\[
P = 2a + 2b
\]

### 4. Substituting \( a \) in Terms of \( b \)
Now, replace \( a \) in the perimeter formula with the expression \( \frac{1}{3}b \):
\[
P = 2\left(\frac{1}{3}b\right) + 2b
\]

### 5. Simplifying the Perimeter Formula
Now let's simplify the expression:
1. Calculate \( 2 \times \frac{1}{3}b \):
\[
P = \frac{2}{3}b + 2b
\]
2. Convert \( 2b \) to a fraction with a denominator of 3:
- \( 2b = \frac{6}{3}b \)
3. Now combine the two terms:
\[
P = \frac{2}{3}b + \frac{6}{3}b = \frac{8}{3}b
\]

### 6. Finding \( b \) Given \( a = 10 \)
You mentioned using \( a = 10 \):
- Using the relation \( a = \frac{1}{3}b \):
\[
10 = \frac{1}{3}b
\]
To find \( b \), multiply both sides by 3:
\[
b = 10 \times 3 = 30
\]

### 7. Calculate the Perimeter
Now plug \( b = 30 \) back into the perimeter formula:
\[
P = \frac{8}{3}(30)
\]
Calculating this gives:
\[
P = \frac{240}{3} = 80
\]

### Conclusion
Thus, the perimeter of A’Leila’s pen is **80 yards**.

If you have any specific parts you want me to clarify further, please let me know!

Answer 11

Got it! Let's write everything out clearly without any parentheses or brackets.

### 1. Relationship Between Sides
You have:
- a = 1/3 b

### 2. Perimeter Formula
The formula for the perimeter P of a rectangle is:
P = a + b + a + b
This simplifies to:
P = 2a + 2b

### 3. Substitute a into the Perimeter Formula
Now we will substitute a with (1/3)b:
P = 2(1/3 b) + 2b

### 4. Simplify the Perimeter Formula
- First, calculate 2(1/3 b):
P = (2/3)b + 2b

- Now convert 2b to a fraction:
2b = (6/3)b

- Now combine the two terms:
P = (2/3)b + (6/3)b
P = (8/3)b

### 5. Finding b Given a = 10
Now, substitute a = 10 into the relationship:
10 = (1/3)b

- Multiply both sides by 3:
b = 10 * 3
b = 30

### 6. Calculate the Perimeter Using b = 30
Now plug b into the perimeter formula:
P = (8/3)(30)

- Now perform the multiplication:
P = 240/3
P = 80

### Conclusion
The perimeter of A’Leila’s pen is 80 yards.

If you need any further explanation or if there's anything else you'd like to clarify, feel free to ask!