The triangle bisector theorem states if a ray bisects an angle of a triangle, then it divides the opposite side of the triangle into segments that are proportional to the other two sides, therefore:
[tex]\frac{x}{8.7}=\frac{16.4}{11.5}[/tex]
Solve for x:
Multiply both sides by 8.7:
[tex]\begin{gathered} 8.7\cdot\frac{x}{8.7}=8.7\cdot\frac{16.4}{11.5} \\ x\approx12.41 \end{gathered}[/tex]
Answer:
x = 12.41
