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Fence Partition Optimization Problem

Fence Partition Optimization Problem
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2014-04-14 05:25
Coordinate GeometryCalculusOptimization
This example demonstrates an optimization problem where a farmer uses 15 meters of fencing to enclose a field partitioned down the center. It involves core math concepts like perimeter, area, and calculus optimization. Constructed using commands such as Intersect, Point, Segment, OrthogonalLine, Polygon, Area, Textfield, Midpoint, CreatePanel for geometric creation and area calculation. Suitable for high school students learning calculus and optimization problems.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(Circle[A, abs(AmountOfFence_1) / 2]) → B
  3. Segment(A, B) → a
  4. Point(a) → C
  5. OrthogonalLine(C, a) → b
  6. OrthogonalLine(D, b) → c
  7. Intersect(b, c) → E
  8. Polygon(C, A, D, E) → poly1, c_1, a_1, d, e
  9. Area(poly1) → Area
  10. Textfield(AmountOfFence_1) → AmountOfFence_2
  11. Midpoint(c_1) → F
  12. Midpoint(d) → G
  13. Segment(F, G) → f
  14. CreatePanel(210) → poly2, g

AI Drawing Prompt Reference

Draw a rectangular area enclosed by 15 meters of fencing with a vertical partition down the middle. Start by creating one side of the rectangle and the midpoint of the vertical partition, then draw the vertical line through the midpoint and complete the rectangle by connecting the remaining sides. Finally, calculate and display the area of the rectangle.
The prompt above was compiled from the original drawing commands and is for reference only.