Heronian triangles

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Hero's formula for the area of a triangle given the length of its three sides a, b, and c is given by:

$A = \sqrt{s(s-a)(s-b)(s-c)},$

where s is half the perimeter of the triangle; that is,

$s=\frac{a+b+c}{2}.$

Heronian triangles are triangles whose sides and area are all integers.

An example is the triangle with sides 3, 4, 5 whose area is 6 (and whose perimeter is 12).

Note that any triangle whose sides are all an integer multiple of 3, 4, 5; such as 6, 8, 10, will also be a Heronian triangle.

Define a Primitive Heronian triangle as a Heronian triangle where the greatest common divisor

of all three sides is 1 (unity).

This will exclude, for example, triangle 6, 8, 10.