Question

calculator
the figure shows △ xyz. overline{xw} is the angle bisector of ∠yxz.
what is wz?
enter your answer as a decimal in the box. do not round your answer.
□ units

Explanation:

Step1: Apply Angle Bisector Theorem

The Angle Bisector Theorem states that if a bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides. So, $\frac{XY}{XZ} = \frac{YW}{WZ}$. Let $WZ = x$, then $YW = 8 - x$ (since $YZ = 8$). We know $XY = 6.5$ and $XZ = 6$. Substituting these values, we get $\frac{6.5}{6} = \frac{8 - x}{x}$.

Step2: Solve the Proportion

Cross - multiply the proportion $\frac{6.5}{6}=\frac{8 - x}{x}$:
\[

$$\begin{align*} 6.5x&=6(8 - x)\\ 6.5x&=48-6x\\ 6.5x + 6x&=48\\ 12.5x&=48\\ x&=\frac{48}{12.5}\\ x& = 3.84 \end{align*}$$

\]

Answer:

3.84