Question

note: the following two triangles are not to scale.
what is the length of \\(\overline{xr}\\)? provide an exact answer or round to two decimal places.
label optional

Explanation:

Step1: Identify similar triangles

Triangles $\triangle BAC$ and $\triangle RPX$ are similar (SAS similarity: $\angle A = \angle P$, $\frac{AC}{PX}=\frac{BC}{RX}=\frac{5}{9}$ is the scale factor ratio of $\triangle BAC$ to $\triangle RPX$).

Step2: Set up proportion for sides

Let $XR = x$. The ratio of corresponding sides is $\frac{AC}{PX} = \frac{BC}{XR}$, so $\frac{5}{9} = \frac{5}{x}$.

Step3: Solve for $x$

Cross-multiply: $5x = 5 \times 9$
Simplify: $x = \frac{45}{5} = 9$

Answer:

9