Question

ajutati maaaa ex 17 ​

Answer 1

Răspuns:

a) CD=9,6 cm; BD=5,4 cm; AD=7,2cm; BC=15cm; AB=9cm; AC=12cm

b) BD=14,4cm; DC=25,6cm; AB=24cm; AC=32cm; AD=19,2cm

Explicație pas cu pas:

-----------------------------------------rezolvare a)-----------------------------------------------

$\frac{CD}{BD} =1\frac{7}{9} =\frac{7+9}{9} =\frac{16}{9} \\\\\\\frac{CD}{BD}=\frac{16}{9} = > 9CD=16BD$

4BD-CD=12 /*4

16BD-4CD=48

Dar 16BD=9CD

deci 9CD-4CD=48

5CD=48

CD=48/5

CD=9,6 cm

4BD-CD=12

4BD=12+9,6=21,6

BD=21,6:4

BD=5,4 cm

Teorema inaltimii:

AD²=BD*CD

$AD=\sqrt{BD*CD} =\sqrt{5,4*9,6} = 7,2\ cm$

BC=BD+CD

BC=5,4+9,6

BC=15cm

TEOREMA CATETEI:

AB²=BD*BC

$AB=\sqrt{BD*BC} =\sqrt{5,4*15} = 9\ cm$

TEOREMA CATETEI:

AC²=DC*BC

$AC=\sqrt{CD*BC} =\sqrt{9,6*15} = 12\ cm$

-----------------------------------------rezolvare b)-----------------------------------------------

$CD-BD=\frac{56}{5} =11,2\\CD=11,2+BD\\\\BC=BD+DC=40\\CD=11,2+BD\\BC=11,2+BD+BD=40\\2BD+11,2=40\\2BD=40-11,2\\2BD=28,8\\BD=28,8:2$

BD=14,4cm

DC=11,2+BD

DC=11,2+14,4

DC=25,6cm

TEOREMA CATETEI:

AB²=BD*BC

$AB=\sqrt{BD*BC} =\sqrt{14,4*40} = 24\ cm$

TEOREMA CATETEI:

AC²=DC*BC

$AC=\sqrt{CD*BC} =\sqrt{25,6*40} = 32\ cm$

Teorema inaltimii:

AD²=BD*CD

$AD=\sqrt{BD*CD} =\sqrt{14,4*25,6} = 19,2\ cm$