Răspuns:
[tex]\textrm{a)} AB=\sqrt{52}\:cm[/tex]
[tex]\textrm{b)} AD = 6\:cm[/tex]
[tex]\textrm{c)}A = 39\:cm^2[/tex]
Explicație pas cu pas:
[tex]BC = BD + DC = 4 + 9 = 13\:cm\\\\ AB^2 = BD\cdot BC\\\\ AB = \sqrt{4\cdot 13} = \sqrt{52}\:cm\\\\ AC^2 = CD \cdot BC \\\\ AC = \sqrt{9\cdot 13} = \sqrt{117}\:cm\\\\ \textrm{AD - inaltime}\\\\ AD = \frac{AB\cdot AC}{BC} = \frac{\sqrt{4\cdot 13} \sqrt{9\cdot 13}}{13} = \frac{2\cdot 3\cdot 13}{13} = 6\:cm\\\\ A = \frac{6\cdot 13}{2} = 3\cdot 13 = 39\:cm^2[/tex]
