Question

In triunghiul ABC,D apartine AB si E apartine CB, astfel incat DE || AC. Stiind ca DB/DA = 2/1, AB =9 cm ,AC=12 cm si BC = 15 cm sa se afle perimetrul triunghiului BDE

Answer 1

ΔABC, DE || AC  => ΔBED ≈ ΔABC

BD/DA=2/1
BD=2DA

BD+DA=AB
2DA+DA=9
3DA=9
DA=3

BD=AB-DA
BD=9-3
BD=6


<=>TFa    => BD/AB=BE/BC=DE/AC <=>

<=> 6/9 = BE/15= DE/12 <=>

2/3=BE/15  =>BE=2*15/3=2*5=10

2/3=DE/12  =>DE=2*12/3=2*4=8

PΔBDE= BD+BE+DE= 6+10+8= 24cm