Question

5. In triunghiul ABC, masura unghiului A= 90 de grade, AD_|_BC, D∈ (BC), se cunosc lungimile a doua segmente:
a) AC= 12 cm, BC =20 cm. Calculati BD, AB,DC,AD.
b) AB= 15 cm, AD= 12 cm. Calculati BD, BC,DC,AC.

6. In triunghiul ABC, masura unghiului A= 90 de grade, AD_|_BC, D∈ (BC), se cunosc lungimile a doua segmente:
a) BD=18 cm, AD= 24 cm. Calculati AB,BC,DC,AC.
b) DC=16 cm, AD= 12 cm. Calculati BD,BD,AB,AC.
c) AB= 15 cm, BD= 9 cm. Calculati AD,BC,DC,AC.

Answer 1

5. In triunghiul ABC, masura unghiului A= 90 de grade, AD_|_BC, D∈ (BC), se cunosc lungimile a doua segmente:
a) AC= 12 cm, BC =20 cm. Calculati BD, AB,DC,AD.
AC²=DCxBC
144=DCx20
DC= 144:20=7,2 cm
BD=20-7,2=12,8 cm
AD=√7,2x12,8=√92,16=9,6 cm
AB=√12,8x20=√256=16 cm
b) AB= 15 cm, AD= 12 cm. Calculati BD, BC,DC,AC.
BD=√AB²-AD²=√15²-14²=√225-144=√81=9 cm
AD²=18xDC
DC=144/9=16 cm
BC=9+16=25 cm
AC=√9x25=√225=15 cm


6. In triunghiul ABC, masura unghiului A= 90 de grade, AD_|_BC, D∈ (BC), se cunosc lungimile a doua segmente:
a) BD=18 cm, AD= 24 cm. Calculati AB,BC,DC,AC.
AB=√18²+24²=√(324+576)=√900=30 cm
DC=24³:18=576:18=32 cm
BC=18+32=50 cm
AC=√32x50=√1600=40 cm

b) DC=16 cm, AD= 12 cm. Calculati BD,BD,AB,AC.
144=BDx16
BD=144:16=9 cm
BC=9+16=25 cm
AB=√9x25=√144=12 cm
AC=√16c25=√400=20 cm

c) AB= 15 cm, BD= 9 cm. Calculati AD,BC,DC,AC.
AD=√15²-9²=√225-81=√144=12 cm
AD²=BDxDC
144=9xDC
DC=144:9=16 cm
BC= 9+16=25 cm
AC=√16c25=√400=20 cm