Let's solve the problem step by step.

Given:

• The length of the rectangular soccer field is 200 meters greater than its width.
• The total length of the boundary (perimeter) is 800 meters.

Let:

• $W$ be the width of the soccer field (in meters).
• $L$ be the length of the soccer field (in meters).

Relations:

1. $L = W + 200$ (since the length is 200 meters more than the width)
2. The perimeter of a rectangle is given by: $\text{Perimeter} = 2 \times (\text{Length} + \text{Width})$ So, $2(L + W) = 800$

Step 1: Substitute $L = W + 200$ into the perimeter equation.

$2((W + 200) + W) = 800$

Step 2: Simplify and solve for $W$.

$2(2W + 200) = 800$ $4W + 400 = 800$ $4W = 800 - 400$ $4W = 400$ $W = \frac{400}{4} = 100$

So, the width $W$ is 100 meters.

Step 3: Find the length $L$.

$L = W + 200 = 100 + 200 = 300 \text{ meters}$

Answer:

• The width of the soccer field is 100 meters.
• The length of the soccer field is 300 meters.

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

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Related Questions:

1. How would the width change if the perimeter increased to 1000 meters?
2. What would the dimensions be if the length was only 150 meters more than the width?
3. How is the formula for the perimeter of a rectangle derived?
4. What is the area of this soccer field?
5. How does the perimeter formula change for a different shape, like a triangle?
6. What would happen to the dimensions if the length was instead 100 meters greater than the width?
7. Can you express the length in terms of width if the relationship was $L = 2W + 50$?
8. How can you verify that the width and length satisfy the perimeter equation?

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Tip: Always check your final solution by substituting the values back into the original equation. This ensures the correctness of your answer.