Question

tu || sv. find rv.
rv =

Explanation:

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

Since \( \overline{TU}\parallel\overline{SV}\), we have \(\frac{RV}{RU}=\frac{RS}{RT}\). Let \(RV = x\), then \(RU=x + 15\), \(RS = 16\), and \(RT=24\). So \(\frac{x}{x + 15}=\frac{16}{24}\).

Step2: Cross - multiply the proportion

Cross - multiplying gives \(24x=16(x + 15)\).
Expanding the right - hand side: \(24x=16x+240\).

Step3: Solve for \(x\)

Subtract \(16x\) from both sides: \(24x-16x=16x + 240-16x\), which simplifies to \(8x=240\).
Divide both sides by \(8\): \(x=\frac{240}{8}=30\).

Answer:

\(30\)