Question

VA ROG COROANA !Se da triunghiul ABC , D apartine ( AB) , E apartine (AC) si DE //BC .
a) Daca AD=6 cm , AC = 8 cm , De = 5cm si BC = 10 cm , calculati AB , BD , AE,EC.
b) Daca AB=18 cm , DB=12 cm , DE = 4cm si AE = 9 cm , calculati AD ,BC , AC si EC .
c)Daca AD = 5 cm , AB = 15 cm , AC = 18 cm si BC=12 cm , calculati AE,DE,DB si EC .
d) Daca AD = 4 cm , DB =6 cm , AC =15 cm si BC=18 cm , calculati AB , AE , EC si DE .
e) Daca AC=14 cm , AD=2,5 cm , DE=4 cm si BC=16 cm , calculati AE , AB , DB si EC .

Answer 1

a)AD/AB=AE/AC=DE/BC
6/AB=AE/8=5/10
AB=6*10/5=12
BD=12-6=6
AE=8*5/10=4
EC=8-4=4

b)AD/AB=AE/AC=DE/BC
AD=18-12=6
6/18=9/AC=4/BC
BC=4*18/6=12
AC =9*18/6=27
EC=27-9=18

c)AD/AB=AE/AC=DE/BC
5/15=AE/18=DE/12
AE=5*18/15=6
DE=5*12/15=4
DB=15-5=10
EC=18-6=12

d)AD/AB=AE/AC=DE/BC
AB=4+6=10 
4/10=AE/15=DE/18
AE=4*15/10=6
DE=18*4/10=7,2
EC=15-6=9
e)AD/AB=AE/AC=DE/BC
2,5/AB=AE/14=4/16
AE=4*14/16=3,5
AB=2,5*16/4=10
DB=10-2,5=7,5
EC=14-3,5=10,5