Question

Daca ΔABC ~ΔDEF,AB=8 cm,AC=10 cm si raportul de asemanare este k=$\frac{2}{5}$,calculati lungimile DE si DF.

Answer 1

  
[tex]\displaystyle \\ \frac{AB}{DE}=\frac{AC}{DF}= \frac{2}{5} \\ \\ \\ \frac{AB}{DE}= \frac{2}{5} ~~\Longrightarrow~~DE = \frac{5AB}{2}= \frac{5 \times 8}{2}= 5 \times 4 = \boxed{20~cm} \\ \\ \\ \frac{AC}{DF}= \frac{2}{5} ~~\Longrightarrow~~DF = \frac{5AC}{2}= \frac{5 \times 10}{2}= 5 \times 5 = \boxed{25~cm} [/tex]