  The perimeter of the rectangular olympic size pool is 406 feet. The length of the pool

         is 15 feet more than three times the width of the pool.







**         Part A:**  What equation could be used to determine the perimeter of the pool?


To determine the perimeter of the pool, we can use the information provided in the problem to set up an equation. 

### Step 1: Define the variables
- Let \( L \) represent the length of the pool (in feet).
- Let \( W \) represent the width of the pool (in feet).

### Step 2: Use the perimeter formula
The perimeter \( P \) of a rectangle is given by:
\[
P = 2L + 2W
\]

Given that the perimeter of the pool is 406 feet, we have:
\[
2L + 2W = 406
\]

### Step 3: Incorporate the relationship between length and width
We are also told that the length \( L \) is 15 feet more than three times the width \( W \). This can be expressed as:
\[
L = 3W + 15
\]

### Step 4: Substitute the length equation into the perimeter equation
Substitute \( L = 3W + 15 \) into the perimeter equation:
\[
2(3W + 15) + 2W = 406
\]

### Final Equation
The equation that could be used to determine the perimeter of the pool is:
\[
2(3W + 15) + 2W = 406
\]

This equation can be simplified and solved to find the width \( W \) of the pool.

Would you like more details, or do you have any questions?

Here are some related questions you might consider:
1. How would you solve the equation \( 2(3W + 15) + 2W = 406 \) to find \( W \)?
2. What is the perimeter equation if the length is four times the width?
3. How does the perimeter formula change if the shape is a square instead of a rectangle?
4. Can you write the equation for perimeter if both length and width are unknown but in terms of their ratio?
5. How would the equation change if the length was instead 20 feet more than three times the width?

**Tip:** When writing equations from word problems, clearly define each variable and ensure that all relationships in the problem are represented in the equation.

Explore how to calculate the perimeter of a rectangular Olympic size pool with a detailed step-by-step solution. Given the relationship between length and width, this problem involves key concepts in geometry and linear equations. Suitable for Grades 7-9.

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