Maximize Triangle Area (Part 2)

Maximize Triangle Area (Part 2)
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2016-01-10 10:02
This example demonstrates how to dynamically adjust triangle vertices to explore the maximum area under a fixed perimeter, involving core math concepts like coordinate geometry, differential calculus (derivatives), integral calculus, and optimization. Key GeoGebra commands used include Function, Polygon, PointIn, and IntegralBetween; objects like f, a, b, c, and poly1 are constructed. Suitable for high school and above, illustrating the application of calculus in geometric optimization problems.

GeoGebra Commands & Parameters

  1. Function(1 / x, 0, 25) → f
  2. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  3. PointIn(poly1) → Pointpoly1
  4. IntegralBetween(((-x)) / ((a * c)) + 1 / a + 1 / c, 1 / x, a, c) → g
  5. IntegralBetween(((-x)) / ((b * c)) + 1 / b + 1 / c, 1 / x, c, b) → h