Heron scalene triangles can be constructed from either combining two Pythagorean triangles or by subtracting two Pythagorean triangles.

I provided a method in Generating scalene Heron triangles — Part 1

Now, let’s construct Heron scalene triangles by subtracting two Pythagorean triangles.

**AB = c**

Here are all scalene Heron triangles when the shortest leg is

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## About benvitalis

math grad - Interest: Number theory

There are also the indecomposable herons that have rational heights for example the {25, 34, 39, 420} triangle {a, b, c, area}. So I do think your statement that all triangles can be constructed above is a bit misleading.

P.

Right. For the indecomposable ones, we need to present an alternative way by using half-angle formulae

I’ll post some ideas on a future blog