Question

rs || tv. find uv.
uv =

Explanation:

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

Since \( \overline{RS}\parallel\overline{TV}\), by the basic proportionality theorem, we have \(\frac{UT}{US}=\frac{UV}{UR}\).
Let \(US = 35\), \(UT = 21\), and \(VR = 8\). Then \(UR=UV + VR=UV + 8\).
Substituting the values into the proportion: \(\frac{21}{35}=\frac{UV}{UV + 8}\).

Step2: Cross - multiply and solve the equation

Cross - multiplying gives \(21(UV + 8)=35UV\).
Expanding the left - hand side: \(21UV+168 = 35UV\).
Subtract \(21UV\) from both sides: \(168=35UV - 21UV\).
Simplify the right - hand side: \(168 = 14UV\).
Divide both sides by 14: \(UV=\frac{168}{14}\).

Answer:

\(12\)