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Triangle Area and Perimeter with Fixed Perimeter

Triangle Area and Perimeter with Fixed Perimeter
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2017-12-11 15:28
TriangleOptimizationGeometric Construction
In collections Mathematics Form 1
This example demonstrates the relationship between the area and perimeter of a triangle with a fixed perimeter. Key math concepts include triangle area, perimeter, geometric construction, and the Pythagorean theorem. It uses commands like Segment, LineBisector, Intersect, Distance, Circle, Ellipse, Point, If, Textfield, DynamicCoordinates, Angle, Polygon, Line, Element, PathParameter, SelectedIndex in GeoGebra to visualize and analyze the geometric properties dynamically. Suitable for high school mathematics education, helping students understand geometric transformations and optimization problems.

GeoGebra Commands & Parameters

  1. Segment(A, B) → j
  2. LineBisector(A, B) → g
  3. Intersect(j, g) → E
  4. Distance(A, B) → AB
  5. Circle(E, SVertex) → e
  6. Intersect(e, g, 2) → J
  7. Ellipse(A, B, J) → k
  8. Intersect(k, g, 2) → D
  9. Point(k) → H
  10. If(Distance[H, J] < 0.2, J, If[Distance[H, D] < 0.2, D, H]) → I
  11. Textfield(PSet) → InputBox1
  12. DynamicCoordinates(H, x(I), y(I)) → C
  13. Distance(A, C) → AC
  14. Distance(B, C) → BC
  15. Segment(A, C) → h
  16. Segment(C, B) → i
  17. Angle(C, B, A) → α
  18. Angle(B, A, C) → β
  19. Polygon(A, C, B) → poly1, b, a, c
  20. Line(A, B) → f
  21. Circle(A, PSet / 2) → p
  22. Intersect(p, f) → F, G
  23. Circle(B, PSet / 2) → q
  24. Intersect(q, f) → K, L
  25. Line(C, g) → m
  26. Intersect(f, m) → M
  27. Circle(A, PSet / 3) → r
  28. Intersect(r, f) → N, O
  29. Element(ListTPanj, IndexOf[Max[ListPanj], ListPanj]) → MaxText
  30. Element(ListTPanj, IndexOf[Min[ListPanj], ListPanj]) → MinText
  31. PathParameter(H) → d
  32. SelectedIndex(Bahasa) → nn
  33. If(nn ≟ 1, " units", " unit") → UTex
  34. If(nn ≟ 1, "units", "unit") → text2
  35. If(nn ≟ 1, "Area = ", "Luas = ") → Tex1
  36. If(nn ≟ 1, "Longest", "Terpanjang") → Tex2
  37. If(nn ≟ 1, "Shortest", "Terpendek") → Tex3