Question

st || ru. find tv. tv =

Explanation:

Step1: Use the triangle - proportionality theorem

Since \( \overline{RU}\parallel\overline{ST}\), by the basic proportionality theorem (Thales' theorem) in \(\triangle VST\), we have \(\frac{VR}{VS}=\frac{VU}{VT}\).
Given \(VR = 16\), \(RS=24\), so \(VS=VR + RS=16 + 24=40\), and \(VU = 18\), let \(TV=x\), then \(VT=x\) and \(TU=x - 18\).
The proportion is \(\frac{16}{40}=\frac{18}{x}\).

Step2: Cross - multiply the proportion

Cross - multiplying the proportion \(\frac{16}{40}=\frac{18}{x}\) gives us \(16x=40\times18\).
First, calculate \(40\times18 = 720\). So, \(16x=720\).

Step3: Solve for \(x\)

Divide both sides of the equation \(16x = 720\) by \(16\). Then \(x=\frac{720}{16}=45\).

Answer:

\(45\)