Question

In ∆ABC construim DE//BC; Dapartine[AB]; Eapartine[AC]; AD=2cm; DB=5cm; EC=10cm. Atunci ce lungimi au AB si AE?

Multumesc!

Answer 1

Aplicam teorema lui Thales

In orice triunghi, o paralela la o latura, imparte celelalte doua laturi in segmente proportionale. 

$\frac{AD}{BD} = \frac{AE}{EC} => \frac{2}{5} = \frac{AE}{10}=>AE*5=2*10=>AE= \frac{2*10}{5}=4 cm$
 
$AB=AD+DB=2+5=7cm$