Question

3) Punctele a, b,c coliniare in aceasta ordine EF mij segmentelor AB si BC daca AE supra BC =4 supra5 . Calculati AB supra AC si BC supra AC .

4) A,B,C coliniare in aceasta ordine astfel incat AC supra BC = 3 supra 4 , BCsupra Bd = 4 supra 9 , AD=64 centimetri . Aflati AB , AC,CD.
5) Punctul O imparte segmentul in raportul 2 supra 3. Calculati OA supra AB si OB supra AB

Answer 1

problema nr.3
faci un segment pe care il vei imparti a,e,b,f,c 
ae=eb si bf=fc
ae/bc=4/5
ae=4bc/5
ab/ac=?
ab=2ae=2*4bc/5=8bc/5
ac=ab+bc=8bc/5+bc
5ac=8bc+5bc
5ac=13bc
ac=13bc/5
ab/ac==8bc/5totul supra 13bc/5=8bc/5*5/13bc=8/13
bc/ac=bc:13bc/5=bc*5/13bc=5/13

problema nr.4

faci un segment ad care are 64 cm
il imparti a,b,c,d
ac/bc=3/4 si bc/bd=4/9
ad=64
ab=?ac=?cd=?
ac=3bc/4
ac=ab+bc
ab+bc+cd=64
3bc/4+cd=64

ne uitam la urmatoarea proportie
bc/bd=4/9
bd=9bc/4
bd=bc+cd
cd=9bc/4-bc
4cd=9bc-4bc
4cd=5bc
cd=5bc/4
3bc/4+5bc/4=64
8bc=64*4
bc=32
cd=5*32/4=40

ab+bc+cd=64
ab=64-32-40
ab=-8

problema nr.5

faci un segment pe care il imparti a,o,b
ao/ab=2/3
ab=ao+ob
ao=2ab/3
ob=ab-ao
ob=ab-2ab/3
3ob=3ab-2ab
3ob=ab
ob=1/3
deci oa/ab=2/3
ob/ab=1/3