Explicație pas cu pas:
ΔABC oarecare
D ∈ AB, 4×BD = AB
E ∈ AC, AE = 15 cm, EC = 5 cm
[tex]4 \times BD = AB = > BD = \frac{AB}{4} \\ AD = AB - BD = AB - \frac{AB}{4} \\ = > \frac{AD}{AB} = \frac{3}{4} [/tex]
[tex]AC = AE + EC = 15 + 5 = 20 \: cm[/tex]
[tex]\frac{AE}{AC} = \frac{15}{20} = > \frac{AE}{AC} = \frac{3}{4} [/tex]
=> DE || BC
[tex]\frac{Aria(ADE)}{Aria(ABC)} = ( \frac{3}{4} )^{2} = \frac{9}{16}[/tex]
