Using the triangle proportionality theorem, the length of segment MF in triangle LMN is: 48 cm.
What is the Triangle Proportionality Theorem?
The triangle proportionality theorem states that when a segment intercepts two sides of a triangle and it is parallel to a third side, then it divides the side proportionally.
The diagram of triangle LMN is shown below. Using the triangle proportionality theorem, we have:
MF/MN = ME/ML
Plug in the values
MF/124 = (31 - 19)/31
MF/124 = 12/31
MF = (12 × 124)/31
MF = 48 cm
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