Question

in △stu, \\( \overline { s t } \parallel \overline { v w } \\). given that \\( u v = 6 \\), \\( w t = 20 \\), and \\( u w = 15 \\), find \\( v s \\).

Explanation:

Step1: Apply the basic proportionality theorem (Thales' theorem)

Since \( \overline{ST}\parallel\overline{VW} \) in \( \triangle STU \), by the basic proportionality theorem, we have \( \frac{UV}{VS}=\frac{UW}{WT} \).

Step2: Substitute the given values into the proportion

Let \( VS = x \). Given \( UV = 6 \), \( UW = 15 \), and \( WT = 20 \). Substituting into \( \frac{UV}{VS}=\frac{UW}{WT} \), we get \( \frac{6}{x}=\frac{15}{20} \).

Step3: Cross - multiply to solve for \( x \)

Cross - multiplying gives \( 15x=6\times20 \). So, \( 15x = 120 \).

Step4: Solve for \( x \)

Dividing both sides by 15: \( x=\frac{120}{15}=8 \).

Answer:

\( VS = 8 \)