Find all non-right angled dissimilar triangles having integer sides and integer area simuntaneously. Are there infinitely many such triangle?

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SuefsSeeltHeRn8 · Accepted Answer

A  =  (  0  ,  0  ),   B  =  (      n    2    −  1  ,  0  ),   C  =  (  0  ,  2  n  ) with   n  ≥  2

Dayami Rose · Accepted Answer

Say you have a triangle with integer sides and area. Let the origin O be one vertex of your triangle, and place another vertex A at (a,0) (with a positive integer). It will be convenient if none of these are obtuse angles of the triangle, so for the argument&#039;s sake, assume OA is the longest side of the triangle.Any third point B with coordinates (x,y) would yield a triangle OAB with integer area as long as y is an integer (base times height divided by 2) (if a is odd, y needs to be even as well). So we need to figure out what such points yield integer sides AB and OB. We have:  |  O  B        |    2    =      x    2    +      y    2        |  A  B        |    2    =  (  a  −  x      )    2    +      y    2    =      a    2    +  2  a  x  +      x    2    +      y    2

Find all non-right angled dissimilar triangles having integer sides and

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