### 1. Relationship Between Sides

Question

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!

how did you get 30 in step 5

Answer 1

In step 5, we started with the relationship between the sides \( a \) and \( b \), which is given by the equation:

\[ a = \frac{1}{3} b \]

You specified that \( a = 10 \). We substitute this value into the equation to find \( b \):

\[ 10 = \frac{1}{3} b \]

To isolate \( b \), we can multiply both sides of the equation by 3 to eliminate the fraction:

\[ 10 \times 3 = b \]

This simplifies to:

\[ b = 30 \]

So, we find that \( b \) equals 30, which is how we arrived at that value in step 5. If you have further questions about this or any other part of the process, feel free to ask!

Answer 2

no brackerts or anything like that

Answer 3

I understand now — you're looking for a clearer explanation without introducing additional notation. Let's simplify that step further.

In step 5, we have the equation connecting \( a \) and \( b \):

1. We know from the problem that \( a \) is equal to \( \frac{1}{3} b \).

2. We are given that \( a = 10 \).

3. So we substitute \( 10 \) in for \( a \):

   \[ 10 = \frac{1}{3} b \]

4. To find \( b \), we want to remove the fraction. We do this by multiplying both sides of the equation by 3:

   \[ 10 \times 3 = b \]

5. This gives us:

   \[ b = 30 \]

So when \( a = 10 \), \( b \) is calculated to be 30. This is how we arrived at the value for \( b \) in the process. If you need further clarification or have more questions, let me know!

Answer 4

no stop no using { [ (

Answer 5

Got it! Let’s explain it without using any brackets or special symbols:

1. We start with the equation that relates a and b: a equals one third of b.
2. We know that a is equal to 10.
3. So we write it out: 10 equals one third of b.
4. To find b, we multiply both sides by 3. This cancels out the fraction on the right side.
5. When we multiply, we get: 10 times 3 equals b.
6. Therefore, b equals 30.

If you have any more questions or need another part clarified, just let me know!