Question

1.Fie ABC un triunghi dreptunghic in A si AD _I_BC,D∈BC.
a)Daca BD=9cm,CD=16cm,aflati AB si AC.
b)Daca BD=3m,AB=6m,aflati CD si AC.
c)Daca BC=9cm,AC=6cm,aflatiAB.
2.Consideram triunghiul ABC,dreptunchic in A, cu inaltimea AD,D∈BC.
a)Daca BD=12,6cm,DC=22,4cm, calculatilungimea laturilorAB si AC.
b)Daca AB=18cm,BD=10,8 cm,calculati lungimea segmentelor DC si AC.

Answer 1

1.Fie ABC un triunghi dreptunghic in A si AD _I_BC,D∈BC.
a)Daca BD=9cm,CD=16cm,aflati AB si AC.
BC=9+16=25
AB=√(9x25)=√225=15 cm
AC=√(16x25)=√400=20 cm
b)Daca BD=3m,AB=6m,aflati CD si AC.
AB²=BDxBC
36=3xBC
BC=12
BD=12-3=9
AC=√(9x12)=√108=6√3
c)Daca BC=9cm,AC=6cm,aflatiAB.
AB=√(9²-6²)=√(81-36)=√45=3√5

2.Consideram triunghiul ABC,dreptunchic in A, cu inaltimea AD,D∈BC.
a)Daca BD=12,6cm,DC=22,4cm, calculatilungimea laturilorAB si AC.
BC=12,6+22,4=35
AB=√(12,6x35)=√441=21 cm
AC=√(22,4x35)=√784=28 cm
b)Daca AB=18cm,BD=10,8 cm,calculati lungimea segmentelor DC si AC.
AB²=BDxBC
18²=10,8xBC
BC=324:10,8
BC=30 cm
DC=30-10,8=19,2 cm
AC=√(30²-18²)=√(900-324)=√576=24 cm