Răspuns:
30 cm
Explicație pas cu pas:
AB = 12 cm, AC = 16 cm
T.P.: BC² = AB² + AC² = 12² + 16² = 144 + 256 = 400 = 20² => BC = 20 cm
BD ≡ DC = BC÷2 => DC = 10 cm
ED ⊥ BC => ΔEDC dreptunghic
ΔEDC ~ ΔBAC =>
[tex]\frac{ED}{AB} = \frac{EC}{BC} = \frac{DC}{AC} \iff \frac{ED}{12} = \frac{EC}{20} = \frac{10}{16} \\ ED = \frac{12 \times 10}{16} \implies ED = 7.5 \: cm \\ EC = \frac{20 \times 10}{16} \implies EC = 12.5 \: cm[/tex]
[tex]P_{\triangle EDC} = ED + DC + EC \\ = 7,5 + 10 + 2,5 = 30 \: cm[/tex]
