Answer:
The correct option is B.
Step-by-step explanation:
From the given figure it is nices that the length of sides AB, BC and AC are 20, 22 and 35. The line AD is angle bisector.
Let the missing value be x.
The Triangle Angle Bisector Theorem states that the angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.
Since AD is angle bisector, therefore
[tex]\frac{AB}{AC}=\frac{BD}{CD}[/tex]
[tex]\frac{20}{35}=\frac{22-x}{x}[/tex]
[tex]20x=35(22-x)[/tex]
[tex]20x=770-35x[/tex]
Add 35x both sides.
[tex]55x=770[/tex]
Divide both sides by 55.
[tex]x=\frac{770}{55}[/tex]
[tex]x=14[/tex]
Therefore, second option is correct.
