A rancher wants to fence in an area of 3,000,000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?


To minimize the total length of the fence needed to enclose a rectangular field of 3,000,000 square feet and divide it in half with a fence down the middle, follow these steps:

1. **Define the Variables:**
   - Let \( L \) be the length of the rectangle.
   - Let \( W \) be the width of the rectangle.
   - The area of the rectangle is given by:
     \[
     L \times W = 3,000,000 \quad \text{square feet}
     \]

2. **Fence Length Calculation:**
   - The total length of the fence will be the perimeter of the rectangle plus the fence down the middle:
   \[
   \text{Total fence length} = 2L + 3W
   \]

3. **Express Width in Terms of Length:**
   - From the area constraint:
   \[
   W

Discover how to calculate the shortest length of fence needed to enclose and divide a 3,000,000 square feet rectangular field. This problem involves geometry concepts such as area calculation and perimeter calculation. Suitable for students in Grades 7-9.

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