Răspuns:
Explicație pas cu pas:
BC=12
Daca m(∡c)=30°⇒ AB=6 si 2AD=AC
Aplicam Pitagora in ΔABC
BC²=AB²+AC²
AC²=144-36=108
AC=6√3⇒ AD=3√3
[tex]A_{ABC}=\frac{AB\cdot AC}{2} =\frac{6\cdot 6\sqrt{3} }{2} =18\sqrt{3}[/tex]
Aplicam in ΔABC teorema catetei
[tex]AC^{2} =CD\cdot BC\\108=CD\cdot12\\CD=9[/tex]
[tex]A_{ADC}=\frac{AD\cdot CD}{2} =\frac{3\sqrt{3} \cdot 9}{2} =\frac{27\sqrt{3} }{2}[/tex]
[tex]A_{ABD}=A_{ABC}-A_{ABD}=18\sqrt{3} -\frac{27\sqrt{3} }{2} =\frac{9\sqrt{3} }{2}\\ \frac{A_{ABD}}{A_{ACD}} =\frac{9\sqrt{3} }{27\sqrt{3} } =\frac{1}{3}[/tex]
