Answer:
64 units
Step-by-step explanation:
Given:
Point M lies between points L and N on Line segment LN.
Length of segment LM is given as =[tex]10x+8[/tex]
Length of segment MN is given as =[tex]5x-4[/tex]
Length of segment LN is given as =[tex]12x+16[/tex]
From the information given we can conclude that the points L,M and N ar co-linear and
[tex]LM+MN=LN[/tex] [ Segment addition postulate as M lies in between L and N]
Substituting the values given to find [tex]x[/tex].
[tex]10x+8+5x-4=12x+16[/tex]
Combining like terms.
[tex]15x+4=12x+16[/tex]
Subtracting both sides by [tex]12x[/tex]
[tex]15x+4-12x=12x+16-12x[/tex]
[tex]3x+4=16[/tex]
Subtracting both sides by 4.
[tex]3x+4-4=16-4[/tex]
[tex]3x=12[/tex]
Dividing both sides by 3.
[tex]\frac{3x}{3}=\frac{12}{3}[/tex]
∴ [tex]x=4[/tex]
Length of segment LN can be found out by substituting [tex]x=4[/tex] in the expression for segment.
⇒ [tex]12(4)+16[/tex]
⇒ [tex]48+16[/tex]
⇒ [tex]64[/tex]
Length of segment LN = 64 units (Answer)
