👤
a fost răspuns

1.Intr-un triunghi dreptunghic ABC, masura unghiului A = 90 grade, AD _|_ BC, D apartine lui BC se da:
a) AD=12cm, CD=8 cm. Calculati BD si BC.
b) AD=24cm, BD=8 cm. Calculati CD si BC.
c) BD=8cm, CD=0,18 m. Claculati AD si BC.

2.Intr-un triunghi dreptunghic ABC, masura unghiului A = 90 grade, AD _|_ BC, D apartine lui BC se da:
a) BD=3,6 dm, CD=6,4 dm. Calculati BC si AD.
b) CD= 7,2 dm, AD= 9,6 dm.Calculati BD si BC.
c) BD= 10,8 dm ,CD=19,2 dm. Calculati BC si AD

Răspuns :

RaluBunny
a) AD=12,CD=8
BD=?   BC=?
[tex] AD^{2} [/tex]=BD×CD⇒[tex] 12^{2} [/tex]=BD×8⇒BD=[tex] \frac{ 12^{2} }{8} [/tex]=[tex] \frac{144}{8}[/tex]=18

b)AD=24,BD=8
CD=?   BC=?
[tex] AD^{2} [/tex]=CD × BD⇒[tex] 24^{2} [/tex]=CD×8⇒CD=[tex] \frac{ 24^{2} }{8}[/tex]=[tex] \frac{576}{8} [/tex]=72

BC=CD+BD=72+8=80 cm

c)BD=8,CD=0.18m=18cm
BC=?   AD=?
BC=BD+CD=8+18=26 cm
[tex] AD^{2} [/tex]=CD×BD=18×8⇒AD=[tex] \sqrt{18*8} [/tex]=12

2.
a) BD=36,CD=64
BC=?  AD=?

BC=BD+CD=36+64=100 cm 
[tex] AD^{2} [/tex]=CD×BD=64×36⇒AD=[tex] \sqrt{64*36} [/tex]=8×6=48 cm

b)
CD=72,AD=96
BD=?   BC=?
[tex] AD^{2}[/tex]=CD×BD⇒[tex] 96^{2} [/tex]=72×BD⇒BD[tex] \frac{ 96^{2} }{72} [/tex]=[tex] \frac{96*96}{72} [/tex] SIMPLIFICAM UNUL DIN CEI 2 DE 96 SI OBTINEM [tex] \frac{4*96}{3} [/tex]=[tex] \frac{384}{3} [/tex]=128
BC=CD+BD=72+128=200 cm

c)
BD=108,CD=192
BC=BD+CD=108+192=300 cm
[tex] AD^{2} [/tex]=BD×CD=108×192⇒AD=[tex] \sqrt{108*192} [/tex]=16×9=144


Alte intrebari