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 = 1.61529+
Found by Pedro Martins
in October 2026. 		Σ s = 1.68627+
Found by Pedro Martins
in July 2026. 		Σ s = 1.76162+
Found by Pedro Martins
in October 2026.

16.
           17.
           18.
Σ s = 1.81473+
Found by Pedro Martins
in October 2026. 		Σ s = 1.86983+
Found by Joost de Winter
in October 2026. 		Σ s = 1.92778+
Found by Pedro Martins
in October 2026.

19.
           20.
           21.
Σ s = 1.98517+
Found by Pedro Martins
in October 2026. 		Σ s = 2.04173+
Found by Pedro Martins
in October 2026. 		Σ s = 2.10003+
Found by Pedro Martins
in October 2026.

22.
           23.
           24.
Σ s = 2.14716+
Found by Pedro Martins
in October 2026. 		Σ s = 2.19806+
Found by Pedro Martins
in October 2026. 		Σ s = 2.24421+
Found by Pedro Martins
in October 2026.

25.
           26.
           27.
Σ s = 2.29239+
Found by Pedro Martins
in October 2026. 		Σ s = 2.34280+
Found by Pedro Martins
in October 2026. 		Σ s = 2.39101+
Found by Pedro Martins
in October 2026.

28.
           29.
           30.
Σ s = 2.44145+
Found by Pedro Martins
in October 2026. 		Σ s = 2.48162+
Found by Pedro Martins
in October 2026. 		Σ s = 2.53081+
Found by Pedro Martins
in October 2026.

31.
           32.
           33.
Σ s = 2.56926+
Found by Pedro Martins
in October 2026. 		Σ s = 2.61222+
Found by Pedro Martins
in October 2026. 		Σ s = 2.65162+
Found by Pedro Martins
in October 2026.

34.
           35.
           36.
Σ s = 2.69513+
Found by Pedro Martins
in October 2026. 		Σ s = 2.73724+
Found by Pedro Martins
in October 2026. 		Σ s = 2.78128+
Found by Pedro Martins
in October 2026.

37.
           38.
           39.
Σ s = 2.81652+
Found by Pedro Martins
in October 2026. 		Σ s = 2.85502+
Found by Pedro Martins
in October 2026. 		Σ s = 2.89096+
Found by Pedro Martins
in October 2026.

40.
           41.
           42.
Σ s = 2.93158+
Found by Pedro Martins
in October 2026. 		Σ s = 2.96966+
Found by Pedro Martins
in October 2026. 		Σ s = 3.00597+
Found by Pedro Martins
in October 2026.

43.
           44.
           45.
Σ s = 3.04532+
Found by Pedro Martins
in October 2026. 		Σ s = 3.08272+
Found by Pedro Martins
in October 2026. 		Σ s = 3.12135+
Found by Pedro Martins
in October 2026.

46.
           47.
           48.
Σ s = 3.15295+
Found by Pedro Martins
in October 2026. 		Σ s = 3.18631+
Found by Pedro Martins
in October 2026. 		Σ s = 3.21968+
Found by Pedro Martins
in October 2026.

49.
           50.
Σ s = 3.25090+
Found by Pedro Martins
in October 2026. 		Σ s = 3.28857+
Found by Pedro Martins
in October 2026.