Answer: The correct option is
(A) 12.
Step-by-step explanation: We are given to find the length of MN from the figure shown.
From the figure, we note that LMN is an isosceles triangle where
[tex]m\angle L=m\angle N=63^\circ,~~LM=3x,~~MN=x+8.[/tex]
We know that
in an isosceles triangle, the lengths of the sides opposite to the equal angles are equal.
So, in triangle LMN, we have
[tex]LM=MN\\\\\Rightarrow 3x=x+8\\\\\Rightarrow 3x-x=8\\\\\Rightarrow 2x=8\\\\\Rightarrow x=\dfrac{8}{2}\\\\\Rightarrow x=4.[/tex]
Therefore, the length of side MN is
[tex]MN=x+8=4+8=12.[/tex]
Thus, the required length of MN is 12 units.
Option (A) is CORRECT.
