Question

find vy.
v w x
5
z
18
y
vy = \boxed{}

Explanation:

Step1: Identify Similar Triangles

Since \( WX \parallel VY \) (implied by the markings, so by the Basic Proportionality Theorem or Similar Triangles), \( \triangle VWZ \sim \triangle VXY \).

Step2: Set Up Proportion

Let \( VY = x \). The ratio of corresponding sides: \( \frac{VW}{VX}=\frac{VZ}{VY} \). Given \( VW = 5 \), \( VX = 15 \), \( VZ = x - 18 \), \( VY = x \). Wait, actually, correct proportion: \( \frac{VW}{VX}=\frac{VZ}{VY} \)? Wait, no, \( VW = 5 \), \( WX = 15 - 5 = 10 \)? Wait, no, \( VX = 15 \), \( VW = 5 \), so \( \frac{VW}{VX}=\frac{VZ}{VY} \). Wait, \( VZ = VY - ZY \), \( ZY = 18 \), so \( VZ = x - 18 \). So \( \frac{5}{15}=\frac{x - 18}{x} \).

Step3: Solve the Proportion

Cross - multiply: \( 5x=15(x - 18) \)
Expand: \( 5x = 15x-270 \)
Subtract \( 5x \) from both sides: \( 0 = 10x - 270 \)
Add 270 to both sides: \( 10x = 270 \)
Divide by 10: \( x = 27 \)

Answer:

\( 27 \)