Question

Se da triunghiul ABC,D apartine AB,E apartine AC si DE||BC.
a)AD=6cm
AC=8cm
DE=5cm
BC=10cm calculati AB,BD,AE,EC
b)AC=14cm
AD=2,5cm
DE=4cm
Bc=16cm calculati AE,AB,DB,EC

Answer 1

a) DE║BC ⇒ΔADE asemenea cu ΔABC
⇒AD/AB=AE/AC=DE/BC=5/10⁽⁵=1/2
AD/AB=1/2 ⇒AB=2×AD=2×6=12 cm
BD=AB-AD=12-6=6 cm
AE/AC=1/2 ⇒AE=AC/2=8/2=4 cm
EC=AC-CE=8-4=4 cm

b) DE║BC ⇒ΔADE asemenea cu ΔABC
⇒AD/AB=AE/AC=DE/BC=4/6⁽²=2/3
AD/AB=2/3 ⇒2AB=3AD⇒AB=3AD/2=3×2,5/2=7,5/2=3,75 cm
BD=AB-AD=3,75-2,5=1,25cm
AE/AC=2/3 ⇒ 3AE=2AC ⇒ AE=2AC/3=2×14/3=28/3=9,(3) cm
EC=1/3AC=1/3×14=14/3=4,(6) cm