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%I #31 Jan 28 2020 11:56:36
%S 24,30,36,42,60
%N Areas of integer-sided triangles whose area equals their perimeter.
%C There are no further terms. Note that without the condition "integer-sided" there are other solutions, such as (9/2, 20, 41/2) which has perimeter and area 45. - _David Wasserman_, Jan 03 2008
%D S. Ainley, Mathematical Puzzles, Problem J8 p. 113, G. Bell & Sons Ltd, London (1977).
%H James Grime and Brady Haran, <a href="https://www.youtube.com/watch?v=UIjeCKPHbso">Superhero Triangles</a>, Numberphile video (2020)
%e The areas or perimeters 24, 30, 36, 42, 60 pertain respectively to triangles with sides (6, 8, 10), (5, 12, 13), (9, 10, 17), (7, 15, 20), (6, 25, 29).
%t m0 = 10 (* = initial max side *); okQ[{x_, y_, z_}] := x <= y <= z && (-x + y + z) (x + y - z) (x - y + z) (x + y + z) == 16 (x + y + z)^2; Clear[f];
%t f[m_] := f[m] = Select[Tuples[Range[m], 3], okQ]; f[m = m0]; f[m = 2 m]; While[f[m] != f[m/2], m = 2 m]; sides = f[m]; Total /@ sides // Sort (* _Jean-François Alcover_, Jul 21 2017 *)
%Y A row of the triangle in A290451.
%K fini,full,nonn
%O 1,1
%A _Lekraj Beedassy_, Sep 10 2004
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