Question

Point M lies between points L and N on Line segment L N .

The space between L and M is 10 x + 8. The space between M and N is 5 x minus 4.
If LN = 12x + 16, what is the length of Line segment L N in units?

16 units
40 units
48 units
64 units

Answer 1

64

Explanation:

Answer 2

64 units

Explanation:

Given:

Point M lies between points L and N on Line segment LN.

Length of segment LM is given as =
`10x+8`

Length of segment MN is given as =
`5x-4`

Length of segment LN is given as =
`12x+16`

From the information given we can conclude that the points L,M and N ar co-linear and

`LM+MN=LN` [ Segment addition postulate as M lies in between L and N]

Substituting the values given to find
`x`.

`10x+8+5x-4=12x+16`

Combining like terms.

`15x+4=12x+16`

Subtracting both sides by
`12x`

`15x+4-12x=12x+16-12x`

`3x+4=16`

Subtracting both sides by 4.

`3x+4-4=16-4`

`3x=12`

Dividing both sides by 3.

`(3x)/(3)=(12)/(3)`

∴
`x=4`

Length of segment LN can be found out by substituting
`x=4` in the expression for segment.

⇒
`12(4)+16`

⇒
`48+16`

⇒
`64`

Length of segment LN = 64 units (Answer)