Answer: The correct option is (D) 24.
Step-by-step explanation: We are given to find the value of x from the given figure, where MO is an angle bisector.
From the figure, we note that
MO is the angle bisector of angle M in ΔLMN, where
ML = x cm, MN = 12 cm, LO = 41 cm and ON = 7 cm.
We have the following theorem :
Angle bisector theorem : An angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle.
Applying the above theorem in the given triangle LMN, we have
[tex]\dfrac{ML}{LO}=\dfrac{MN}{ON}\\\\\\\Rightarrow \dfrac{x}{14}=\dfrac{12}{7}\\\\\Rightarrow x=\dfrac{12\times 14}{7}\\\\\Rightarrow x=24.[/tex]
Thus, the required value of x is 24.
Option (D) is CORRECT.
