Question

rs || tv. find rv.
rv =

Explanation:

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

Since \( \overline{RS}\parallel\overline{TV} \), we have \( \frac{ST}{SU}=\frac{RV}{RU} \). Let \( RV = x \), then \( RU=x + 39 \), \( ST = 27 \), \( SU=27 + 18=45 \).
So, \( \frac{27}{45}=\frac{x}{x + 39} \).

Step2: Cross - multiply the equation

Cross - multiplying gives \( 27(x + 39)=45x \).
Expanding: \( 27x+1053 = 45x \).

Step3: Solve for \( x \)

Subtract \( 27x \) from both sides: \( 1053=45x - 27x \).
\( 18x = 1053 \).
Divide both sides by 18: \( x=\frac{1053}{18}=58.5 \).

Answer:

\( 58.5 \)