LO−→ bisects <NLM, LM = 12, NO = 3 and LN = 8. What is the value of x? Drawing is not to scale. Please show ALL work in order to receive full credit for the problem. (3 points)
To find the value of x, we need to use the properties of a bisector.
First, let's draw a diagram to help us visualize the problem.
We have triangle NLM, where NO = 3, LN = 8, and LM = 12. The angle bisector from O intersects LM at point P. Let's label the length of NP as x.
L
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N______O______M
According to the angle bisector theorem, we know that the ratio of the lengths of the segments formed by the angle bisector is equal to the ratio of the lengths of the opposite sides.
In other words,
NP / NO = LP / LO
Substituting the given values, we have:
x / 3 = (12 - 8) / 8
x / 3 = 4 / 8
x / 3 = 1 / 2
Cross-multiplying, we get:
2x = 3
x = 3/2 = 1.5
So the value of x is 1.5.