Answer:
a. AB/BC = DE/EF
4/6 = 8/EF
2/3 = 8/EF
2*EF = 8*3
2EF = 24
2EF/2 = 24/2
DF = DE + EF
= 8 + 12
b. AB/BC =DE/EF
8/6 = DE/10
4/3 = DE/10
4*10 = DE*3
40 = 3DE
40/3 = 3DE/3
= 40/3 + 10
= 40/3 + 30/3
c. AB/AC = DE/DF
10/18 = DE/20
5/9 = DE/20
5*20 = DE*9
100 = 9DE
100/9 = 9DE/9
BC = AC - AB
= 18 - 10
EF = DF - DE
= 20 - 100/9
= 180/9 - 100/9
d. AB/AC = DE/DF
15/25 = DE/30
3/5 = DE/30
3*30 = DE*5
90 = 5DE
90/5 = 5DE/5
= 25 - 15
= 30 - 18
e. DE/DF = AB/AC
16/30 = AB/28
8/15 = AB/28
8*28 = AB*15
224 = 15AB
224/15 = 15AB/15
= 28 - 224/15
= 420/15 - 224/15
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Answers & Comments
Answer:
a. AB/BC = DE/EF
4/6 = 8/EF
2/3 = 8/EF
2*EF = 8*3
2EF = 24
2EF/2 = 24/2
EF = 12
DF = DE + EF
= 8 + 12
DF = 20
b. AB/BC =DE/EF
8/6 = DE/10
4/3 = DE/10
4*10 = DE*3
40 = 3DE
40/3 = 3DE/3
DE = 40/3 = 13 1/3 = 13.33
DF = DE + EF
= 40/3 + 10
= 40/3 + 30/3
DF = 70/3 = 23 1/3 = 23.33
c. AB/AC = DE/DF
10/18 = DE/20
5/9 = DE/20
5*20 = DE*9
100 = 9DE
100/9 = 9DE/9
DE = 100/9 = 11 1/9 = 11.11
BC = AC - AB
= 18 - 10
BC = 8
EF = DF - DE
= 20 - 100/9
= 180/9 - 100/9
EF = 80/9 = 8 8/9 = 8.89
d. AB/AC = DE/DF
15/25 = DE/30
3/5 = DE/30
3*30 = DE*5
90 = 5DE
90/5 = 5DE/5
DE = 18
BC = AC - AB
= 25 - 15
BC = 10
EF = DF - DE
= 30 - 18
EF = 12
e. DE/DF = AB/AC
16/30 = AB/28
8/15 = AB/28
8*28 = AB*15
224 = 15AB
224/15 = 15AB/15
AB = 224/15 = 14 14/15 = 14.93
BC = AC - AB
= 28 - 224/15
= 420/15 - 224/15
= 196/15 = 13 1/15 = 13.07