The ratio of the three segment can be found using the segment addition
property.
Reasons:
The given parameters are;
A, B, C, and D are on a straight line.
AB:BD = 1 : 5
AC:CD = 7 : 11
Required:
The value of AB : BC : CD
Solution:
[tex]\displaystyle \frac{AB}{BD} = \frac{1}{5}[/tex]
[tex]\displaystyle \frac{AC}{CD} = \frac{7}{11}[/tex]
Therefore;
[tex]\displaystyle \mathbf{\frac{AB}{BC + CD} } = \frac{1}{5}[/tex]
[tex]\displaystyle \mathbf{\frac{AB + BC}{CD}} = \frac{7}{11}[/tex]
AB + BD = (1 + 5 ) × x = (6 × x) units
AC + CD = 7 + 11 = 18 units
AB + BD = AC + CD (length of the same line)
Therefore;
(6 × x) units = 18 units
x = 3
3 × (AB + BD) = 3 × 6 = 18
AB = 1 × 3 = 3 units
AC = 7 units
Therefore;
BC = AC - AB = 7 units - 3 units = 4 units
BC = 4 units
CD = 18 units - 7 units = 11 units
CD = 11 units
AB : BC : CD = 3 : 4 : 11
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