Answer:
a = 4.5
WX is an angle bisector.
We used the Angle Bisector Theorem to find the value of a.
Step-by-step explanation:
In a triangle, an angle bisector is a line segment that divides one of the interior angles into two congruent angles.
The given diagram shows triangle XYZ with a line segment bisecting angle X that intersects side YZ at point W. Therefore, line segment WX is an angle bisector.
To determine the value of a (the length of side XY), we can use the Angle Bisector Theorem. This theorem states that in a triangle, an angle bisector divides the side opposite the bisected angle into segments that are proportional to the lengths of the other two sides of the triangle.
Therefore:
[tex]\dfrac{a}{6}=\dfrac{3}{4}[/tex]
To solve for a, multiply both sides by 6 and simplify:
[tex]\dfrac{a}{6}\cdot 6=\dfrac{3}{4}\cdot 6[/tex]
[tex]a=\dfrac{18}{4}[/tex]
[tex]a=\dfrac{9}{2} = 4.5[/tex]
Therefore, the value of a is 4.5.
