Question

find ux.
ux =
submit

Explanation:

Step1: Identify Similar Triangles

Since \( VY \parallel WX \), by the Basic Proportionality Theorem (Thales' theorem), \( \triangle UVY \sim \triangle UWX \). So, the ratios of corresponding sides are equal: \( \frac{UV}{UW} = \frac{UY}{UX} \).

Step2: Calculate \( UW \)

\( UW = UV + VW = 12 + 9 = 21 \). Let \( UX = x \), then \( UY = x - 21 \).

Step3: Set Up Proportion

Substitute into the ratio: \( \frac{12}{21} = \frac{x - 21}{x} \).

Step4: Solve for \( x \)

Cross - multiply: \( 12x = 21(x - 21) \)
Expand: \( 12x = 21x - 441 \)
Subtract \( 12x \): \( 0 = 9x - 441 \)
Add \( 441 \): \( 9x = 441 \)
Divide by 9: \( x = \frac{441}{9}=49 \).

Answer:

\( 49 \)