Respuesta :

calculista

Answer:

Option D. LN=64 units

Step-by-step explanation:

step 1

Find the value of x

we know that

LN=LM+MN -----> equation A

we have

LN=12x+16

LM=10x+8

MN=5x-4

substitute the values in the equation A

12x+16=(10x+8)+(5x-4)

Solve for x

12x+16=15x+4

15x-12x=16-4

3x=12

x=4

step 2

Find the value of LN

LN=12x+16

LN=12(4)+16=64 units

The length of LN in units is 64 units

Calculating length of a line

From the question, we are to determine the length of LN

In the given diagram

/LM/ = 10x + 8

/MN/ = 5x - 4

We can observe that

/LM/ + /MN/ = /LN/

From the given information,

/LN/ = 12x + 16

Therefore,

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

Solving for x

15x +4 = 12x + 16

Then,

15x - 12x = 16 - 4

3x = 12

Thus,

x = 4

Then, substitute the value of x into LN = 12x + 16

LN = 12(4) + 16

LN = 48 + 16

LN = 64 units

Hence, the length of LN in units is 64 units

Learn more on Calculating length of line here: https://brainly.com/question/11562184

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