Let's solve the problem step by step.

Step 1: Define the variables

Let:

• $L$ = Length of the pool (in feet)
• $W$ = Width of the pool (in feet)

Step 2: Set up the equations based on the given information

1. The perimeter of the rectangle is given by: $\text{Perimeter} = 2L + 2W = 406 \text{ feet}$

2. The length is 15 feet more than three times the width: $L = 3W + 15$

Step 3: Substitute the second equation into the first equation

Substitute $L = 3W + 15$ into the perimeter equation: $2(3W + 15) + 2W = 406$

Step 4: Simplify and solve for $W$

Expand and combine like terms: $6W + 30 + 2W = 406$ $8W + 30 = 406$ Subtract 30 from both sides: $8W = 376$ Divide by 8: $W = 47 \text{ feet}$

Step 5: Find the length $L$

Substitute $W = 47$ back into the equation for $L$: $L = 3(47) + 15 = 141 + 15 = 156 \text{ feet}$

Step 6: Conclusion

The width of the pool is 47 feet, and the length of the pool is 156 feet.

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

Here are some related questions you might consider:

1. What would the area of the pool be?
2. How would the dimensions change if the perimeter was increased by 20 feet?
3. What is the ratio of the length to the width of the pool?
4. How would the length change if the width was doubled?
5. How can you express the length of the pool as a function of the perimeter and width?

Tip: Always double-check your substitution in equations to ensure accuracy in the final results.