Question

tu || sv. find rv.
18
t s 6 r
28
u
rv =

Explanation:

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

Since \( \overline{TU}\parallel\overline{SV}\), we have the proportion \(\frac{RS}{RT}=\frac{RV}{RU}\).
First, find \(RT\): \(RT = 18\), \(RS=RT - SR=18 - 6=12\), and \(RU = RV + 28\).
The proportion becomes \(\frac{6}{18}=\frac{RV}{RV + 28}\).

Step2: Cross - multiply the proportion

Cross - multiplying gives \(6(RV + 28)=18RV\).
Expand the left - hand side: \(6RV+168 = 18RV\).

Step3: Solve for \(RV\)

Subtract \(6RV\) from both sides: \(168=18RV - 6RV\).
So, \(12RV = 168\).
Divide both sides by 12: \(RV=\frac{168}{12}\).

Answer:

\(RV = 14\)