Răspunsuri

2014-02-01T16:07:51+02:00
 \frac{AB}{DE} = \frac{AC}{DF} = \frac{BC}{EF} = \frac{6}{DE} = \frac{16}{DF} = \frac{8}{EF} = \frac{6+16+8}{60} = \frac{30}{60} = \frac{1}{2}
 \frac{AB}{DE} = \frac{1}{2} => \frac{6}{DE} = \frac{1}{2} => DE=12
 \frac{AC}{DF} = \frac{1}{2} => \frac{16}{DF} = \frac{1}{2} => DF=32
 \frac{BC}{EF} = \frac{1}{2} =>  \frac{8}{EF} = \frac{1}{2} => EF=16

E corecta rezolvarea Dianei!
Multumesc! :D
You are welcome!
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2014-02-01T18:16:54+02:00
      Daca 2 triunghiuri sunt asemenea, atunci rapoartele dintre laturilor lor sunt proportionale.

 Δ ABC ~  Δ DEF <=>  \frac{AB}{DE} = \frac{AC}{DF} = \frac{BC}{EF} =  \frac{AB + AC + BC}{DE + DF + EF} =  \frac{6+16+8}{60} =  \frac{30}{60} =  \frac{1}{2}

 Deci  \frac{AB}{DE} =  \frac{1}{2} =>  \frac{6}{DE} =  \frac{1}{2}  <=> DE = 12

           \frac{AC}{DF} = \frac{1}{2} =>  \frac{16}{DF} = \frac{1}{2} <=> DF = 32

           \frac{BC}{EF} = \frac{1}{2} => \frac{8}{EF} = \frac{1}{2} <=> EF = 16

      Puteam observa de la inceput ca perimetrul triunghiul ABC este 30 cm, iar perimetrul triunghiului DEF = 60 cm (deci de 2 ori mai mare). Aceste triunghiuri fiind asemenea => Laturile triunghiului DEF au lungimile duble fata de lungimile laturilor triunghiului ABC.