Question

In triunghiul ABC m(A)=90 grade construim AD perpendicular pe BC, D apartine (BC)
a) Daca AD= 6cm si AB=AC, Aflati BC și AB

b) Daca BC 27 cm si CD=2BD, calculati BD, DC, AD.

Answer 1

a) AB=AC=>ABC isoscel=>m(∡C)=45=>ADC isoscel=>AD=DC
m(∡B)=45=>ADB isoscel=>AD=BD
BC=BD+DC=2AD=12cm
$AB^{2}+ AC^{2}= BC^{2}$=>2$AB^{2}= 12^{2}=144=\ \textgreater \ AB^{2}=72=\ \textgreater \ AB=6 \sqrt{2}$

b)BC=BD+DC=BD+2BD=3BD=27=>BD=9
DC=2BD=18
$AD^{2}=BD*DC$(teorema inaltimii)=>$AD^{2}=9*18= 162=\ \textgreater \ AD=9 \sqrt{2}$

Answer 2

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