Question

uv || rt. find rs.
rs =

Explanation:

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

Since \( \overline{UV}\parallel\overline{RT}\), we have \(\frac{VR}{RS}=\frac{UT}{TS}\). Given \(UT = 13\), \(TS=39\), and \(VR = 10\).

Step2: Substitute the values into the proportion

Let \(RS=x\). Then \(\frac{10}{x}=\frac{13}{39}\). Cross - multiply: \(13x=10\times39\).

Step3: Solve for \(x\)

\(13x = 390\), so \(x=\frac{390}{13}=30\).

Answer:

\(30\)