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Find Equal Perimeters

Find Equal Perimeters
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2014-04-16 21:03
FunctionCoordinate GeometryGeometric Construction
This example demonstrates dynamically finding the height of a rectangle where the perimeters are equal using GeoGebra. It involves core math concepts like perimeter calculation, equation solving, and geometric transformations. Key GeoGebra commands/objects used include OrthogonalLine, Point, Intersect, Polygon, Circle, and Segment. Suitable for high school mathematics teaching to understand the relationship between perimeter, area, and geometric transformations.

GeoGebra Commands & Parameters

  1. OrthogonalLine(A, yAxis) → b
  2. Point(xAxis) → B
  3. OrthogonalLine(B, b) → c
  4. Intersect(b, c) → C
  5. Intersect(xAxis, yAxis) → D
  6. Polygon(A, C, B, D) → poly1, a_1, c_1, b_1, d
  7. Circle(E, r / 2) → e
  8. Circle(E_1, r_1 / 2) → e_1
  9. Polygon(D, A, C, B) → poly2, d_1, a_2, c_2, b_2
  10. OrthogonalLine(E, xAxis) → g
  11. Intersect(e, g, 2) → F
  12. Intersect(e, e_1, 1) → G
  13. Intersect(e, g, 1) → H
  14. Segment(F, H) → h

AI Drawing Prompt Reference

Draw a rectangle with two circles, one centered above the rectangle on a perpendicular line and the other below, both intersecting the sides of the rectangle. Connect the intersection points to form new segments, demonstrating the dynamic relationship where the perimeters of the rectangle and circles are equal.
The prompt above was compiled from the original drawing commands and is for reference only.