Question

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

Answer 1

a) AD=12,CD=8
BD=?   BC=?
$AD^{2}$=BD×CD⇒$12^{2}$=BD×8⇒BD=$\frac{ 12^{2} }{8}$=$\frac{144}{8}$=18

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

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

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

2.
a) BD=36,CD=64
BC=?  AD=?

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

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

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