If the perimeter of the runway is 11,160 m, write an equation for the perimeter of the runway in terms of the variable w.

To find an equation for the perimeter of the runway in terms of its width, \( w \), given that the perimeter is 11,160 meters, we can use the expression for the length we found earlier.

### Step-by-step Solution:

1. **Define the variables:**
   - Width of the runway: \( w \) meters.
   - Length of the runway: \( l = 50w + 1500 \) meters.

2. **Perimeter of a rectangle formula:**
   The perimeter \( P \) of a rectangle is given by:
   \[
   P = 2l + 2w
   \]

3. **Substitute the length \( l \) in terms of \( w \):**
   Substitute \( l = 50w + 1500 \) into the perimeter formula:
   \[
   P = 2(50w + 1500) + 2w
   \]

4. **Simplify the equation:**
   Expand and simplify the terms:
   \[
   P = 100w + 3000 + 2w
   \]
   \[
   P = 102w + 3000
   \]

5. **Given the perimeter is 11,160 meters:**
   Set the equation equal to 11,160:
   \[
   102w + 3000 = 11160
   \]

### Final Equation:

The equation for the perimeter of the runway in terms of the width \( w \) is:

\[
\boxed{102w + 3000 = 11160}
\]

Would you like to solve this equation for the width or need more clarification? Here are some related questions:

1. What is the width of the runway if the perimeter is 11,160 meters?
2. How would the perimeter change if the width increased by 10 meters?
3. What would the equation look like if the length expression changed?
4. How does altering the length formula affect the perimeter equation?
5. Can the runway's width be found if only the perimeter and a different length formula are given?

**Tip:** In perimeter problems, always substitute the known expressions for dimensions before setting up equations; it simplifies the calculations significantly!

Learn how to derive the equation for the perimeter of a runway in terms of its width, given specific dimensions and constraints. This problem involves using the formula for the perimeter of a rectangle and algebraic manipulation. Suitable for Grades 7-9 students.

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