Answer:
Option D.
Step-by-step explanation:
Given information: Line a is the perpendicular bisector of KM.
Point L is the midpoint of KM.
If a line passes through a vertex of a triangle, is perpendicular bisector of the base of the triangle then the triangle is always an isosceles triangle.
[tex]9x-5=7x+7[/tex]
Isolate variable terms.
[tex]9x-7x=5+7[/tex]
[tex]2x=12[/tex]
Divide both sides by 2.
[tex]x=6[/tex]
The value of x is 6.
[tex]KL=6x+4\Rightarrow 6(6)+4=40[/tex]
We need to find the length of KM.
[tex]KM=2KL[/tex] (L is the midpoint of KM)
[tex]KM=2(40)[/tex]
[tex]KM=80[/tex]
Therefore, the correct option is D.
