Squares in Triangles

The following pictures show n squares with the largest possible sum of sides packed inside a unit equilateral triangle.

1.
           2.
           3.
Σ s = 2√3–3 = .46410+
Trivial. 		Σ s = 18–10√3 = .67949+
Found by Erich Friedman
in June 2026. 		Σ s = (63–31√3)/10 = .93064+
Found by Jonathan Viquerat
in June 2026.

4.
           5.
           6.
Σ s = 1.07948+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 1.22888+
Found by Jonathan Viquerat
in June 2026. 		Σ s = (327–171√3)/22 = 1.40087+
Found by Jonathan Viquerat
in June 2026.

7.
           8.
           9.
Σ s = 1.51535+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 1.63240+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 1.75582+
Found by Jonathan Viquerat
in September 2026.

10.
           11.
           12.
Σ s = 1.86607+
Found by Haowei Lin
in July 2026. 		Σ s = 1.96484+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 2.05916+
Found by Jonathan Viquerat
in June 2026.

13.
           14.
           15.
Σ s = 2.15473+
Found by Haowei Lin
in July 2026. 		Σ s = 2.24353+
Found by Jonathan Viquerat
in September 2026. 		Σ s = 2.33280+
Found by Haowei Lin
in July 2026.

16.
           17.
           18.
Σ s = 2.41865+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 2.49817+
Found by Haowei Lin
in July 2026. 		Σ s = 2.57855+
Found by Haowei Lin
in July 2026.

19.
           20.
           21.
Σ s = 2.65121+
Found by Haowei Lin
in July 2026. 		Σ s = 2.72549+
Found by Pedro Martins
in October 2026. 		Σ s = 2.80200+
Found by Haowei Lin
in July 2026.

22.
           23.
           24.
Σ s = 2.87413+
Found by Joost de Winter
in October 2026. 		Σ s = 2.94482+
Found by Pedro Martins
in October 2026. 		Σ s = 3.07428+
Found by Jonathan Viquerat
in October 2026.

25.
           26.
           27.
Σ s = 3.07753+
Found by Pedro Martins
in October 2026. 		Σ s = 3.14137+
Found by Pedro Martins
in October 2026. 		Σ s = 3.20642+
Found by Pedro Martins
in October 2026.

28.
           29.
           30.
Σ s = 3.26855+
Found by Pedro Martins
in October 2026. 		Σ s = 3.33257+
Found by Pedro Martins
in October 2026. 		Σ s = 3.39587+
Found by Pedro Martins
in October 2026.

31.
           32.
           33.
Σ s = 3.45802+
Found by Pedro Martins
in October 2026. 		Σ s = 3.51301+
Found by Pedro Martins
in October 2026. 		Σ s = 3.57114+
Found by Pedro Martins
in October 2026.

34.
           35.
           36.
Σ s = 3.62861+
Found by Pedro Martins
in October 2026. 		Σ s = 3.68232+
Found by Pedro Martins
in October 2026. 		Σ s = 3.73662+
Found by Pedro Martins
in October 2026.

37.
           38.
           39.
Σ s = 3.79352+
Found by Pedro Martins
in October 2026. 		Σ s = 3.84934+
Found by Pedro Martins
in October 2026. 		Σ s = 3.90530+
Found by Pedro Martins
in October 2026.

40.
           41.
           42.
Σ s = 3.95527+
Found by Pedro Martins
in October 2026. 		Σ s = 4.00767+
Found by Pedro Martins
in October 2026. 		Σ s = 4.05784+
Found by Pedro Martins
in October 2026.

43.
           44.
           45.
Σ s = 4.10877+
Found by Pedro Martins
in October 2026. 		Σ s = 4.15850+
Found by Pedro Martins
in October 2026. 		Σ s = 4.20931+
Found by Pedro Martins
in October 2026.

46.
           47.
           48.
Σ s = 4.25711+
Found by Pedro Martins
in October 2026. 		Σ s = 4.30451+
Found by Pedro Martins
in October 2026. 		Σ s = 4.35631+
Found by Pedro Martins
in October 2026.

49.
           50.
Σ s = 4.40169+
Found by Pedro Martins
in October 2026. 		Σ s = 4.44802+
Found by Pedro Martins
in October 2026.