Question

ajutați ma ex 18....​

Answer 1

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.

Answer 2

Răspuns:

CD=16cm

BD=9cm

BC=25cm

AB=15cm

AC=20cm

Explicație pas cu pas:

$\frac{BD}{CD} =0,5625\\\\BD=0,5625*CD$

TEOREMA INALTIMII:

AD²=BD*CD

144=0,5625*CD*CD

CD²=144:0,5625=256

$CD=\sqrt{256}=16$

BD=0,5625*CD

BD=0,5625*16

BD=9cm

BC=BD+DC

BC=16+9

BC=25cm

TEOREMA CATETEI:

AB²=BD*BC

$AB=\sqrt{BD*BC} =\sqrt{9*25} = 15\ cm$

TEOREMA CATETEI:

AC²=DC*BC

$AC=\sqrt{CD*BC} =\sqrt{16*25} = 20\ cm$