A farmer has a rectangular field with a length that is twice its width. The perimeter of the field is 600 meters. What is the area of the field? The area of the field is ____ square meters.
Answer & Analysis
Analysis
Question Analysis
This problem requires students to set up and solve a system of linear equations based on the given information about the dimensions of a rectangular field and then calculate the area.
Key Concept Explanation
The key concepts include setting up a system of equations, solving the system, and using the solution to find the area of the rectangle.
Step-by-step Solution
1. Define the variables: Let be the width and be the length of the field.
2. Write the system of equations based on the given information:
3. Substitute into the second equation:
4. Simplify and solve for :
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