あのー盛り上がってるとこ申し訳ないんだけど
こんなんみつけたんだけど

https://www.research.ibm.com/haifa/ponderthis/download/Feb2004_dima.pdf

lengths of the sides of ABC ? primitive right triangle: ( 352, 135, 377) ,
lengths of the sides of DEG - right triangle: ( 360, 66, 366) ,
lengths of the sides of DEF ? isosceles triangle: DE=DF=366 , EF=132 ,
indeed = 864 , PABC PDEF = S ABC = S DEF = 23760 .