MathPlotAI Logo MathPlotAI

The Largest Triangle

The Largest Triangle
Loading the math board and drawing, please wait…
2015-11-17 12:25
TriangleOptimizationGeometric Construction
In collections Algebra II|CH7: Polynomial Functions
This example demonstrates how to find the largest triangle under given conditions through geometric construction. Key mathematical concepts include properties of triangles and area formulas. It utilizes commands like Polygon, Distance, Rotate, Angle, Ray, Intersect, OrthogonalLine, Circle, and Segment in GeoGebra. Suitable for high school mathematics education, particularly in geometric construction and optimization.

GeoGebra Commands & Parameters

  1. Polygon(A, D, E, F) → poly1, h_1, w_1, h_2, w_2
  2. Distance(B, A) → distanceBA
  3. Distance(D, A) → distanceDA
  4. Rotate(A, a, B) → A'
  5. Angle(A, B, A') → α
  6. Ray(B, A') → b_3
  7. Intersect(w_2, b_3) → C
  8. OrthogonalLine(C, b_3) → c
  9. Circle(C, 11) → d
  10. Intersect(d, c, 2) → G
  11. OrthogonalLine(G, c) → e
  12. Intersect(e, h_2) → H
  13. Segment(B, H) → f
  14. Intersect(c, w_1) → I
  15. Segment(B, I) → g
  16. Segment(B, C) → h_4
  17. Segment(C, G) → i
  18. Segment(G, H) → j
  19. Segment(C, I) → k
  20. Polygon(B, C, G, H) → poly2, b_1, c_1, g_1, h_3
  21. Polygon(B, C, I) → poly3, i_1, b_2, c_2
  22. Segment(A, C) → b
  23. Segment(A, B) → h