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The problem asks us to find the correct equation that represents the given information about the rectangular field.

1. The width of the rectangular field is given as \( y \) feet.
2. The length of the field is four times the width, so the length is \( 4y \) feet.
3. The perimeter of the field is 86 feet.

The formula for the perimeter \( P \) of a rectangle is:
\[
P = 2(\text{length} + \text{width})
\]

Substituting the values:
\[
86 = 2(4y + y)
\]

Simplifying:
\[
86 = 2(5y)
\]
\[
86 = 10y
\]

Solving for \( y \):
\[
y = \frac{86}{10} = 8.6 \, \text{feet}
\]

Now, let's check which equation represents this situation. Since the perimeter formula simplifies to \( 86 = 10y \), the correct equation should follow from that logic.

- **Option A:** \( y + y + 4y + 4y = 86 \) – This simplifies to \( 10y = 86 \), which is correct.

Thus, **Option A** is the correct equation.

Do you want further details or have any questions?

### Related Questions:
1. How do you calculate the area of the rectangular field with the given dimensions?
2. If the width \( y \) was increased by 2 feet, how would the perimeter change?
3. What would happen to the perimeter if the length was tripled instead of being four times the width?
4. How can you generalize the perimeter equation for any multiple of the width?
5. How would the perimeter change if the dimensions were doubled?

### Tip:
When solving problems involving perimeter, always apply the formula \( 2(\text{length} + \text{width}) \) to ensure accuracy in combining terms.

A rectangular field is y feet wide. The length of the field is four times longer than the width. If the perimeter of the field is 86 feet, which of the following equations represents the given information?

Solve a problem involving the perimeter of a rectangle, where the length is four times the width and the perimeter is 86 feet. Use the perimeter formula P = 2(length + width) to find the correct equation. This problem is suitable for students in Grades 6-8.

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