Răspuns :
Răspuns:
CD=16 cm
BD=9 cm.
AB=15 cm.
AC=20 cm.
BC=25 cm.
Explicație pas cu pas:
BD/CD=0,5625 ⇒BD=CD·0,5625
AD=12 cm ⇒AD²=CD·BD ⇒144=CD·CD·0,5625=CD²·0,5625 ⇒144=CD²·0,5625 ⇒CD²=144:0,5625=256 ⇒CD=16 cm
BD=CD·0,5625=16·0,5625=9 cm. BD=9 cm.
AB²=AD²+BD²=144+81=225 ⇒AB=15 cm.
AC²=BC²-AB²=25²-15²=625-225=400 ⇒AC=20 cm.
BC=BD+CD=9+16=25 cm BC=25 cm.
Răspuns:
CD=16cm
BD=9cm
BC=25cm
AB=15cm
AC=20cm
Explicație pas cu pas:
[tex]\frac{BD}{CD} =0,5625\\\\BD=0,5625*CD[/tex]
TEOREMA INALTIMII:
AD²=BD*CD
144=0,5625*CD*CD
CD²=144:0,5625=256
[tex]CD=\sqrt{256}=16[/tex]
BD=0,5625*CD
BD=0,5625*16
BD=9cm
BC=BD+DC
BC=16+9
BC=25cm
TEOREMA CATETEI:
AB²=BD*BC
[tex]AB=\sqrt{BD*BC} =\sqrt{9*25} = 15\ cm[/tex]
TEOREMA CATETEI:
AC²=DC*BC
[tex]AC=\sqrt{CD*BC} =\sqrt{16*25} = 20\ cm[/tex]