Question

what is the length of \\(\overline{zy}\\)? provide an exact answer or round to two decimal places.

Explanation:

Step1: Identify similar triangles

Triangles $YZW$ and $RPX$ are similar (corresponding angles equal, AA similarity).

Step2: Set up proportion

Corresponding sides are proportional: $\frac{ZY}{RX} = \frac{ZW}{PX}$

Step3: Substitute known values

$\frac{ZY}{3} = \frac{4}{5}$

Step4: Solve for $ZY$

$ZY = 3 \times \frac{4}{5}$

Answer:

$\frac{12}{5}$ or $2.40$