Pentagons in Triangles

The following pictures show n regular pentagons packed inside a unit equilateral triangle, so that the total sum of the sides of the pentagons is as large as possible.

1.
           2.
           3.
Σ s = 6/(3+3√5+√(6(5+√5))) = .36815+
Trivial.
  		Σ s = .50395+
Found by Jonathan Viquerat
in June 2026. 		Σ s = .73031+
Found by Jonathan Viquerat
in June 2026.

4.
           5.
           6.
Σ s = .82930+
Found by Jonathan Viquerat
in June 2026. 		Σ s = .92964+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 1.07719+
Found by Jonathan Viquerat
in June 2026.

7.
           8.
           9.
Σ s = 1.15736+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 1.23720+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 1.32596+
Found by Jonathan Viquerat
in June 2026.

10.
           11.
           12.
Σ s = 1.41659+
Found by Pedro Martins
in July 2026. 		Σ s = 1.48404+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 1.55059+
Found by Jonathan Viquerat
in June 2026.

13.
           14.
           15.
Σ s = 1.61442+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 1.68627+
Found by Pedro Martins
in July 2026. 		Σ s = 1.76065+
Found by Pedro Martins
in July 2026.

16.
           17.
           18.
Σ s = 1.81323+
Found by Joost de Winter
in September 2026. 		Σ s = 1.86792+
Found by Pedro Martins
in July 2026. 		Σ s = 1.92521+
Found by Joost de Winter
in September 2026.

19.
           20.
           21.
Σ s = 1.98444+
Found by Pedro Martins
in July 2026. 		Σ s = 2.04069+
Found by Joost de Winter
in September 2026. 		Σ s = 2.09694+
Found by Joost de Winter
in September 2026.

22.
           23.
           24.
Σ s = 2.13766+
Found by Joost de Winter
in September 2026. 		Σ s = 2.18781+
Found by Joost de Winter
in September 2026. 		Σ s = 2.22272+
Found by Joost de Winter
in October 2026.

25.
           26.
           27.
Σ s = 2.28871+
Found by Joost de Winter
in September 2026. 		Σ s = 2.32778+
Found by Joost de Winter
in September 2026. 		Σ s = 2.38202+
Found by Joost de Winter
in September 2026.

28.
           29.
           30.
Σ s = 2.43274+
Found by Joost de Winter
in September 2026. 		Σ s = 2.46856+
Found by Joost de Winter
in September 2026. 		Σ s = 2.49815+
Found by Joost de Winter
in October 2026.

31.
           32.
           33.
Σ s = 2.55258+
Found by Joost de Winter
in September 2026. 		Σ s = 2.59323+
Found by Joost de Winter
in September 2026. 		Σ s = 2.64274+
Found by Joost de Winter
in September 2026.

34.
           35.
           36.
Σ s = 2.67451+
Found by Joost de Winter
in October 2026. 		Σ s = 2.72703+
Found by Joost de Winter
in September 2026. 		Σ s = 2.77921+
Found by Joost de Winter
in September 2026.

37.
           38.
           39.
Σ s = 2.80598+
Found by Joost de Winter
in September 2026. 		Σ s = 2.83595+
Found by Joost de Winter
in September 2026. 		Σ s = 2.88052+
Found by Joost de Winter
in September 2026.

40.
           41.
           42.
Σ s = 2.91778+
Found by Joost de Winter
in September 2026. 		Σ s = 2.94528+
Found by Joost de Winter
in October 2026. 		Σ s = 2.98718+
Found by Joost de Winter
in September 2026.

43.
           44.
           45.
Σ s = 3.01900+
Found by Joost de Winter
in September 2026. 		Σ s = 3.06208+
Found by Joost de Winter
in September 2026. 		Σ s = 3.10421+
Found by Joost de Winter
in September 2026.

46.
           47.
           48.
Σ s = 3.13957+
Found by Joost de Winter
in September 2026. 		Σ s = 3.16681+
Found by Joost de Winter
in September 2026. 		Σ s = 3.20384+
Found by Joost de Winter
in September 2026.

49.
           50.
Σ s = 3.22739+
Found by Joost de Winter
in October 2026. 		Σ s = 3.24414+
Found by Joost de Winter
in October 2026.