Little explorations with HP calculators (no Prime)

[Han]

The claim that "the shape does not matter" is not a trivial statement. It is fairly easy to deduce if we are comparing two triangles who have the same base length and the same height. Then the areas of two such triangles are the same. However, two triangles with different side lengths and having the same area (of 24) can still satisfy the conditions of the problem. Thus a solution using any assumptions such as x=y=z or even just x=z must include some explanation why such a solution extends to the general case when x is not equal to z (or y) while still maintaining an area of 24.