Question

sw || tv. find tu.

tu =

Explanation:

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

Since \( \overline{SW}\parallel\overline{TV}\), we have \(\frac{SU}{TU}=\frac{WU}{VU}\). Let \(TU = x\), then \(SU=27 + x\) and \(VU=28 - 12=16\).

Step2: Set up the proportion equation

\(\frac{27 + x}{x}=\frac{28}{16}\)
Cross - multiply: \(16(27 + x)=28x\)
Expand: \(432+16x = 28x\)
Subtract \(16x\) from both sides: \(432=28x - 16x\)
Simplify: \(432 = 12x\)
Solve for \(x\): \(x=\frac{432}{12}=36\)

Answer:

\(36\)