Explicație pas cu pas:
[tex]<BAC = 90, <ABC = 60 \\ => < BCA=30, < BAD= 30[/tex]
[tex]AB=2×BD=2×12= > AB = 24 \: cm[/tex]
[tex]AD^{2} = AB^{2} - BD^{2} = {24}^{2} - {12}^{2} = 432 = > AD = 12 \sqrt{3}\: cm [/tex]
[tex]AD^{2} = BD \times DC \\ DC = \frac{AD^{2}}{BD} = \frac{432}{12} = > DC = 36 \: cm[/tex]
[tex]BC = BD + DC = 12 + 36 = > BC = 48 \: cm [/tex]
[tex]AC^{2} = BC^{2} - AB^{2} = 48^{2} - 24^{2} = 1728 = > AC = 24 \sqrt{3} \: cm [/tex]
[tex]P = AB+BC+AC=24+48+24 \sqrt{3} \\ = > P = 24(3 + \sqrt{3}) \: cm [/tex]
