Answer:
[tex]x=14[/tex], [tex]BD=88[/tex], [tex]BC=27[/tex], [tex]CD=61[/tex].
The value of CD is 61 units.
Step-by-step explanation:
Given information: BD = 7x-10, BC = 4x-29, and CD = 5x-9,
From the given figure it is clear that Points B, C and D collinear. Point C lies on line segment BD.
[tex]BD=BC+CD[/tex]
Substitute BD = 7x-10, BC = 4x-29, and CD = 5x-9 in the above equation.
[tex]7x-10=(4x-29)+(5x-9)[/tex]
On combining like terms we get
[tex]7x-10=(4x+5x)+(-29-9)[/tex]
[tex]7x-10=9x-38[/tex]
Add 38 on both sides.
[tex]7x-10+38=9x[/tex]
[tex]7x+28=9x[/tex]
Subtract 7x from both sides.
[tex]28=9x-7x[/tex]
[tex]28=2x[/tex]
Divide both sides by 2.
[tex]14=x[/tex]
Therefore the value of x is 14.
[tex]BD = x-10=7(14)-10=88[/tex]
The value of BD is 88 units.
[tex]BC = 4x-29=4(14)-29=27[/tex]
The value of BC is 27 units.
[tex]CD = 5x-9=5(14)-9=61[/tex]
The value of CD is 61 units.
