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 =![10x+8](https://tex.z-dn.net/?f=10x%2B8)
Length of segment MN is given as =![5x-4](https://tex.z-dn.net/?f=5x-4)
Length of segment LN is given as =![12x+16](https://tex.z-dn.net/?f=12x%2B16)
From the information given we can conclude that the points L,M and N ar co-linear and
[ Segment addition postulate as M lies in between L and N]
Substituting the values given to find
.
![10x+8+5x-4=12x+16](https://tex.z-dn.net/?f=10x%2B8%2B5x-4%3D12x%2B16)
Combining like terms.
![15x+4=12x+16](https://tex.z-dn.net/?f=15x%2B4%3D12x%2B16)
Subtracting both sides by ![12x](https://tex.z-dn.net/?f=12x)
![15x+4-12x=12x+16-12x](https://tex.z-dn.net/?f=15x%2B4-12x%3D12x%2B16-12x)
![3x+4=16](https://tex.z-dn.net/?f=3x%2B4%3D16)
Subtracting both sides by 4.
![3x+4-4=16-4](https://tex.z-dn.net/?f=3x%2B4-4%3D16-4)
![3x=12](https://tex.z-dn.net/?f=3x%3D12)
Dividing both sides by 3.
![\frac{3x}{3}=\frac{12}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%7D%7B3%7D%3D%5Cfrac%7B12%7D%7B3%7D)
∴ ![x=4](https://tex.z-dn.net/?f=x%3D4)
Length of segment LN can be found out by substituting
in the expression for segment.
⇒ ![12(4)+16](https://tex.z-dn.net/?f=12%284%29%2B16)
⇒ ![48+16](https://tex.z-dn.net/?f=48%2B16)
⇒ ![64](https://tex.z-dn.net/?f=64)
Length of segment LN = 64 units (Answer)