It seems you've uploaded an image. Let me first analyze it and then provide a detailed response based on its content. PIL import Image

Load and display the image to analyze its content

img_path = "/mnt/data/1733462503298jmyrji8o.jpg" image = Image.open(img_path) image.show()I have opened the image, but I need to extract and analyze its mathematical content. Let me process it further to provide a solution or explanation. Attempting OCR to extract text or mathematical content from the image import pytesseract

Extract text from the image using OCR

text = pytesseract.image_to_string(image) textThe image contains a word problem involving the perimeter of a rectangular pool. Here's a summary of the problem:

• Width of the pool is represented by $p$ feet.
• Length of the pool is 1 more than 4 times the width, so the length is expressed as $4p + 1$.
• You are asked to find two expressions that represent the perimeter of the pool, with several options provided for selection.

Understanding the Formula:

The formula for the perimeter $P$ of a rectangle is given by:

$P = 2 \times (\text{length}) + 2 \times (\text{width})$

Using the given expressions:

• Length = $4p + 1$
• Width = $p$

Thus, the perimeter $P$ can be written as:

$P = 2 \times (4p + 1) + 2 \times p$

Simplifying:

$P = 2(4p + 1) + 2p = 8p + 2 + 2p = 10p + 2$

Now, let's review the provided options:

1. $10p + 1$
2. $5p + 1$
3. $26p + 1$
4. $4(p + 4p + 1)$
5. $10p + 2$
6. $2p + 4p + 1$

Correct Expressions:

From the calculation above, the correct expression for the perimeter is $10p + 2$. Therefore, the correct option is:

• E. $10p + 2$

This matches the formula for the perimeter based on the provided dimensions of the pool.

Would you like more detailed steps, or do you have any questions about this? Here are some follow-up questions:

1. How would the perimeter change if the width was doubled?
2. What is the formula for the area of the pool?
3. How can we find the perimeter if the length and width are given in numerical values?
4. If a second border of tiles is added, how would the perimeter change?
5. How does the relationship between the length and width affect the perimeter formula?

Tip: When dealing with geometry problems involving perimeter, always check if the dimensions are given in terms of a variable, and apply the perimeter formula accordingly.