Question

Daca triunghiul ABC este asemenea triunghiului DEF, AB=8cm, DE=6cm, DF=12cm, EF=9cm, calculati DE si EF
Puteti sa explicati detaliat va rog pt ca nu inteleg

Answer 1

1.

ΔABC~ΔDEF de unde rezulta ca vom forma un raport de asemanare:

$\frac{AB}{DE} = \frac{BC}{EF}= \frac{AC}{DF}$

Acum ca am format raportul,inlocuim:

[tex] \frac{8}{6} = \frac{BC}{9} = \frac{AC}{12} \\\\ =\ \textgreater \ BC= \frac{9*8}{6} =\ \textgreater \ BC=12 cm\\\\ [/tex]

Am aflat BC-ul,acum aflam AC din proportia:

$\frac{BC}{9} = \frac{AC}{12} =\ \textgreater \ \frac{12}{9} = \frac{AC}{12} =\ \textgreater \ AC= \frac{12*12}{9} =\ \textgreater \ AC= \frac{48}{3} =\ \textgreater \ AC=16cm$

2. Daca triunghiul ABC este asemenea DEF iar AB-16 cm AC-14cm BC-18 si DE-28cm calculati DE SI EF.

ΔABC~ΔDEF

=>[tex] \frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}\ \textless \ =\ \textgreater \ \frac{16}{28} = \frac{18}{EF} = \frac{14}{DF} \\\\ =\ \textgreater \ EF= \frac{18*28}{16} =\ \textgreater \ EF=31,5\\\\ =\ \textgreater \ DF= \frac{14*31,5}{18} =\ \textgreater \ DF=24,5[/tex]