Question

se considera un triunghi ABC cu BC=25 si punctele D apaartine AB,E apartine AC astfel incat DE paralel cu BC si AD/DB=2/3.
Aflati lungimea segmentului DE

Answer 1

[tex]\it \dfrac{AD}{DB} = \dfrac{2}{3} \stackrel{derivare}{\Longrightarrow} \dfrac{AD}{DB+AD} = \dfrac{2}{3+2} \Rightarrow \dfrac{AD}{AB} = \dfrac{2}{5}\ \ \ \ (*) \\\;\\ \\\;\\ DE||BC \stackrel{T.f.a.}{\Longrightarrow} \Delta ADE \sim \Delta ABC \Rightarrow \dfrac{AD}{AB} = \dfrac{DE}{BC} \stackrel{(*)}{\Longrightarrow} \dfrac{2}{5} = \dfrac{DE}{25} \Rightarrow \\\;\\ \\\;\\ \Rightarrow DE = 10\ cm[/tex]