The question you provided asks for an equation to determine the perimeter of a rectangular field. Let’s break it down:

Given:

• The perimeter of the rectangular field is 260 feet.
• The length is 10 feet more than twice the width of the field.

Step-by-Step Analysis:

1. Perimeter formula for a rectangle is: $P = 2L + 2W$ where $L$ is the length, and $W$ is the width.

2. Length relationship: The length $L$ is 10 feet more than twice the width, so we can express the length as: $L = 2W + 10$

3. Substitute this expression for $L$ into the perimeter formula: $260 = 2(2W + 10) + 2W$

4. Now simplify this equation: $260 = 4W + 20 + 2W$ $260 = 6W + 20$

5. Subtract 20 from both sides: $240 = 6W$

6. Finally, divide by 6 to solve for $W$: $W = 40 \text{ feet}$

Conclusion:

The correct equation from the options given is:

$2w + 2(2w + 10) = 260$

So, the correct option is the fourth one.

Do you want further details on solving this equation, or have any other questions?

Here are five follow-up questions that might help expand on this topic:

1. How would the equation change if the length was 5 feet more than twice the width?
2. What if the perimeter was 300 feet instead of 260 feet?
3. How can we determine the length after finding the width?
4. What is the area of the field once the width and length are known?
5. Can you create a graph that shows the relationship between width and perimeter?

Tip: Always check if an equation can be simplified before solving. It helps prevent errors!