A098030 Areas of integer-sided triangles whose area equals their perimeter.

24, 30, 36, 42, 60

Offset: 1

Author

Lekraj Beedassy, Sep 10 2004

Keywords

• fini
• full
• nonn

Comments

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

Examples

			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).
		

References

• S. Ainley, Mathematical Puzzles, Problem J8 p. 113, G. Bell & Sons Ltd, London (1977).

Links

• James Grime and Brady Haran, Superhero Triangles, Numberphile video (2020)

Crossrefs

A row of the triangle in A290451.

Programs

Mathematica

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];
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 *)