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 = 2.72533+
Found by Haowei Lin
in July 2026. 		Σ s = 2.80200+
Found by Haowei Lin
in July 2026.

22.
           23.
           24.
Σ s = 2.86771+
Found by Jonathan Viquerat
in September 2026. 		Σ s = 2.93551+
Found by Jonathan Viquerat
in September 2026. 		Σ s = 3.07428+
Found by Jonathan Viquerat
in October 2026.

25.
           26.
           27.
Σ s = 3.07428+
Found by Jonathan Viquerat
in October 2026. 		Σ s = 3.12931+
Found by Jonathan Viquerat
in October 2026. 		Σ s = 3.19309+
Found by Jonathan Viquerat
in October 2026.

28.
           29.
           30.
Σ s = 3.25567+
Found by Joost de Winter
in September 2026. 		Σ s = 3.31762+
Found by Jonathan Viquerat
in October 2026. 		Σ s = 3.37768+
Found by Joost de Winter
in September 2026.

31.
           32.
           33.
Σ s = 3.43660+
Found by Joost de Winter
in September 2026. 		Σ s = 3.49696+
Found by Jonathan Viquerat
in October 2026. 		Σ s = 3.55280+
Found by Jonathan Viquerat
in October 2026.

34.
           35.
           36.
Σ s = 3.61080+
Found by Jonathan Viquerat
in October 2026. 		Σ s = 3.66504+
Found by Jonathan Viquerat
in October 2026. 		Σ s = 3.72651+
Found by Jonathan Viquerat
in October 2026.

37.
           38.
           39.
Σ s = 3.77661+
Found by Jonathan Viquerat
in October 2026. 		Σ s = 3.83564+
Found by Joost de Winter
in October 2026. 		Σ s = 3.89690+
Found by Joost de Winter
in October 2026.

40.
           41.
           42.
Σ s = 3.94514+
Found by Joost de Winter
in September 2026. 		Σ s = 3.97961+
Found by Joost de Winter
in October 2026. 		Σ s = 4.03088+
Found by Joost de Winter
in September 2026.

43.
           44.
           45.
Σ s = 4.09447+
Found by Joost de Winter
in September 2026. 		Σ s = 4.13207+
Found by Joost de Winter
in October 2026. 		Σ s = 4.15485+
Found by Joost de Winter
in October 2026.

46.
           47.
           48.
Σ s = 4.21523+
Found by Joost de Winter
in September 2026. 		Σ s = 4.25283+
Found by Joost de Winter
in October 2026. 		Σ s = 4.27661+
Found by Joost de Winter
in October 2026.

49.
           50.
Σ s = 4.33069+
Found by Joost de Winter
in September 2026. 		Σ s = 4.36829+
Found by Joost de Winter
in October 2026.