Little explorations with HP calculators (no Prime)

[Han]

(04-07-2017 02:52 PM)Gerson W. Barbosa Wrote:  

(04-07-2017 12:57 PM)SlideRule Wrote:  IF the base and the height remain constant, the AREA of the triangle is also constant, irrespective of an alteration of the "shape" of the original triangle

Exactly! As long as the base and the height are kept constant, the area won't change.

When you assume that x=y=z, this triangle does not have the same base and height as a triangle for which x, y, and z are not simultaneously equal. The side AC might remain 2x (we may view this as the "base"), but the height of the triangle for which x=y=z will NOT be equal to the height of the triangle for which x, y, and z are not simultaneously equal.