Question

In ΔABC cu BC=15 cm, AB=12 cm se duce DE II AB, D ∈ (AC), E ∈ (BC) astfel incat AD= 3 cm si DC= 6 cm. Sa se afle perimetrul ΔDEC

Answer 1

DC/AC=CE/BC=DE/AB
DC=6
AD=3
AC=6+3=9
6/9=CE/15=DE/12
CE=6x15/9=10
DE=6x12/9=8
P=6+10+8=24 cm

Answer 2

DE//AB => ABC asemenea DEC

=> $\frac{AC}{DC} = \frac{BC}{EC}= \frac{AB}{DE}$

=>$\frac{3+6}{6} = \frac{15}{EC} = \frac{12}{DE}$

=>$\frac{9}{6} = \frac{15}{EC} = \frac{12}{DE}$

=>$EC= \frac{6*15}{9} =10$ cm

=>$DE= \frac{6*12}{9} =8$ cm

$P_{DEC}$= DE+EC+DC = 8+10+6 = 24 cm