??$解:①如圖①, EF//AB$??
??$所以\frac {EF}{AB}=\frac {CI}{CD}$??
??$AB=\sqrt{82+62}= 10, CD=\frac {8×6}{10}= 4.8$??
??$設(shè)正方形邊長為:x\ \mathrm {cm} ,$??
??$\frac {x}{10}=\frac {4.8}{4}-8,$??
??$解得x= \frac {120}{37}$??
??$②如圖②,可得△AED∽△DFB∽△ACB$??
??$設(shè)正方形邊長為n\ \mathrm {cm}$??
??$則AD=\frac {5}{3}n,BD=\frac {5}{4}n$??
??$AB=\frac {5}{3}n+\frac {5}{4}n=10$??
??$解得n=\frac {24}{7}$??
??$\frac {120}{37}≈3.2;\frac {24}{7}≈3.4$??
??$所以\frac {24}{7}>\frac {120}{37}$??
??$所以圖②中正方形即為所求,邊長為\frac {24}{7}$??