Question

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

Answer 1

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 =$10x+8$

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.

$\frac{3x}{3}=\frac{12}{3}$

∴ $x=4$

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)

Answer 2

Answer:

64

Step-by-step explanation: