Question

Fie triunghiul ABC cu masura unghiului A de 90 grade si AD perpendicular pe BC D apartine lui BC
a Daca BD=3 cm si BC=12 cm calculati AB si AC
Daca BD=9 cm si CD=16 cm calculati AB si AC
Daca DC/BC=1/4 si AC=8 cm calculati BC si AB
DacaBD/DC=3/5 si BC=16 cm calculati  BD DC AB si AC

Answer 1

Daca BD=3 cm si BC=12 cm calculati AB si AC
Din teorema catetei:
AB²=BC*BD=12*3=36
AB=6

DC=BC-BD=12-3=9
AC²=DC*BC=9*12=108
AC=6√3
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Daca BD=9 cm si CD=16 cm calculati AB si AC
BC=BD+DC=9+16=25

AB²=BC*BD=25*9=225
AB=15

AC²=DC*BC=16*25=400
AC=20
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Daca DC/BC=1/4 si AC=8 cm calculati BC si AB
BC=4DC

AC²=DC*BC⇒ 8²=DC*4DC
64=4*DC²
DC²=16
DC=4
BC=4*4⇒BC=16

BD=BC-DC=16-4=12
AB²=BC*BD=16*12=192
AB=8√3


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DacaBD/DC=3/5 si BC=16 cm calculati  BD DC AB si AC