A Heronian triangle with sidelengths c, e and b + d, and height a, all integers.
An integer triangle or integral triangle is a triangle all of whose side lengths are integers. A rational triangle is one whose side lengths are rational numbers; any rational triangle can be rescaled by the lowest common denominator of the sides to obtain a similar integer triangle, so there is a close relationship between integer triangles and rational triangles.
Sometimes other definitions of the term rational triangle are used: Carmichael (1914) and Dickson (1920) use the term to mean a Heronian triangle (a triangle with integral or rational side lengths and area);[1] Conway and Guy (1996) define a rational triangle as one with rational sides and rational angles measured in degrees—the only such triangles are rational-sided equilateral triangles.[2]
^Carmichael, R. D. (1959) [1914]. "Diophantine Analysis". In R. D. Carmichael (ed.). The Theory of Numbers and Diophantine Analysis. Dover Publications. pp. 11–13].
^Conway, J. H., and Guy, R. K., "The only rational triangle", in The Book of Numbers, 1996, Springer-Verlag, pp. 201 and 228–239.
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