Question

vw || su. find tv.
tv =

Explanation:

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

Since \( \overline{VW}\parallel\overline{SU}\), by the basic proportionality theorem, \(\frac{TS}{SW}=\frac{TU}{UV}\). Let \(TV = x\), then \(TU=x - 48\) and \(SW = 60\), \(TS = 24\).

Step2: Set up the proportion equation

\(\frac{24}{60}=\frac{x - 48}{48}\)
Cross - multiply: \(24\times48=60\times(x - 48)\)
\(1152 = 60x-2880\)

Step3: Solve for \(x\)

Add \(2880\) to both sides: \(1152 + 2880=60x\)
\(4032 = 60x\)
Divide both sides by \(60\): \(x=\frac{4032}{60}=67.2\)

Answer:

\(67.2\)