Question

wx || vy. find uw. u v w y x 13 19 38 uw =

Explanation:

Step1: Identify Similar Triangles

Since \( WX \parallel VY \), by the Basic Proportionality Theorem (Thales' theorem), \( \triangle UVY \sim \triangle UWX \) (AA similarity, as corresponding angles are equal due to parallel lines).

Step2: Set Up Proportion

For similar triangles, the ratios of corresponding sides are equal. So, \( \frac{UV}{UW} = \frac{UY}{UX} \). We know \( UV = 13 \), \( UY = 19 \), and \( UX = UY + YX = 19 + 38 = 57 \). Let \( UW = x \), then \( UV = x - VW \), but actually \( UW = UV + VW \), wait, no—\( UV \) is a segment on \( UW \), so \( UV = 13 \), \( UW = 13 + VW \), but using the similarity ratio: \( \frac{13}{x} = \frac{19}{57} \).

Step3: Solve for \( x \)

Cross - multiply: \( 19x = 13\times57 \). Calculate \( 13\times57 = 741 \). Then \( x=\frac{741}{19}=39 \).

Answer:

\( 39 \)