Răspuns:
135 cm
Explicație pas cu pas:
[tex]ctg \hat C = \frac{CD}{AD} \iff \frac{CD}{AD} = \frac{4}{3} \\ \implies \bf CD = \frac{4AD}{3}[/tex]
[tex]AD^{2} = CD \cdot BD \iff AD^{2} = \frac{4AD}{3} \cdot 20.25 \\ \implies \bf AD = 27 \: cm[/tex]
[tex]CD = \frac{4 \times 27}{3} \implies \bf CD = 36 \: cm \\ [/tex]
[tex]BC = CD + BD = 36 + 20,25 \\ \implies \bf BC = 56,25 \ cm[/tex]
[tex]AB^{2} = BD \cdot BC = 20,25 \cdot 56,25 \\ \implies \bf AB = 33,75 \ cm[/tex]
[tex]AC^{2} = CD \cdot BC = 36 \cdot 56,25 \\ \implies \bf AC = 45 \ cm[/tex]
[tex]P_{\triangle ABC} = AB + AC + BC = \\ = 33,75 + 45 + 56,25 = \bf 135 \ cm[/tex]
