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))) = .36816+
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 = 1.41512+
Found by Jonathan Viquerat
in June 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 = 1.68397+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 1.75447+
Found by Jonathan Viquerat
in June 2026.

16.
           17.
           18.
Σ s = 1.81239+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 1.86480+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 1.92401+
Found by Jonathan Viquerat
in June 2026.

19.
           20.
Σ s = 1.97526+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 2.03147+
Found by Jonathan Viquerat
in June 2026.