Question

rezolvarea problemei 10

d8d6d6759caf36f96554d40e1ad05653.pdf

Answer 1

$DE||AC\Rightarrow \Delta ACB\sim\Delta EDB\Rightarrow\dfrac{AC}{BE}=\dfrac{CB}{DB}\Rightarrow\dfrac{18}{6}=\dfrac{CB}{8-CB}$

Adunam numaratorii la numitori si obtinem:

$\dfrac{18}{24}=\dfrac{CB}{8}\Rightarrow CB=\dfrac{8\cdot18}{24}=6\ cm$

$A_{ABC}=\dfrac{BC\cdot AC}{2}=\dfrac{6\cdot18}{2}=54\ cm^2$

Answer 2

DE || AC=> ΔABC ~ ΔBDE=>AC\BE=CB\DB
 (INLOCUIM CE CUNOASTEM)
<=> 18/6=CB/DB <=>

DC=DB+CB=>DB=DC - CB<=>8-CB

<=>16/8=CB/8-CB (FACEM PRODUSUL MEZILOR SI AL EXTREMILOR= INMULTIM PE DIAGONALA)
<= >6CB=18(8-CB)
<=>6CB=18*8-18CB
<=>6CB=144-18CB
6CB+18CB=144=>24CB=144=>CB=144/24=>CB=6

A ΔABC=C1*C2/2, UNDE C1,C2 REPREZINTA CATETA 1 RESPECTIV CATETA 2
A ΔABC=BC*AC/2<=>A ΔABC=6*18/2=>A ΔABC=54