Answer: LM = 57
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Step-by-step explanation:
A median of a triangle goes from a vertex to the midpoint of the opposite side. The three medians of this triangle are these segments:
The three medians intersect at the centroid point, which is point Q.
It turns out that the centroid cuts each median such that LQ is twice as long compared to QM. We can say
LQ = 2*QM
Applying the segment addition postulate and substitution, we then get,
LQ + QM = LM
2QM + QM = LM
3QM = LM
LM = 3QM
Now let's use LQ = 38 to find QM
LQ = 2*QM
38 = 2*QM
QM = 38/2
QM = 19
This then means,
LM = 3QM
LM = 3*19
LM = 57
Segment LM is 57 units long.