Question

fie unttiunghi ABC ,D apartine lui AB , E apartine lui AC DE paralel BC . Daca AD: DB= 2:3 si AC= 50 cm determinati lungimea segmentului AE.

Answer 1

[tex]DE||BC \xrightarrow{T.F.A}\dfrac{AD}{AB}=\dfrac{AE}{AC}=\dfrac{DE}{BC}\Rightarrow \dfrac{AD}{AB-AD}=\dfrac{AE}{AC-AE}\Rightarrow\\ \Rightarrow \dfrac{AD}{BD}=\dfrac{AE}{EC}=\dfrac{2}{3}\Rightarrow EC=\dfrac{3}{2}\cdot AE\\ E\in(AC)\Rightarrow AE+EC=AC\\ ~~~~~~~~~~~~~~~~~~~AE+\dfrac{3}{2}\cdot AE=50|\cdot 2\\ ~~~~~~~~~~~~~~~~~~~2AE+3AE=100\\ ~~~~~~~~~~~~~~~~~~~5AE=100\Rightarrow \boxed{AE=20\ cm}[/tex]