Question

tu || sv. find uv.
39
26
r
s
t
66
v
u
uv =

Explanation:

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

Since \( \overline{TU}\parallel\overline{SV}\), we have \(\frac{RS}{ST}=\frac{RV}{VU}\). First, find \(RS\): \(RS = 39 - 26=13\). Let \(UV=x\), then \(RV = 66 - x\).

Step2: Set up the proportion equation

Substitute the values into the proportion \(\frac{RS}{ST}=\frac{RV}{VU}\), we get \(\frac{13}{26}=\frac{66 - x}{x}\).

Step3: Cross - multiply

Cross - multiplying gives \(13x=26(66 - x)\).

Step4: Expand the right - hand side

\(13x = 1716-26x\).

Step5: Solve for \(x\)

Add \(26x\) to both sides: \(13x + 26x=1716\), \(39x = 1716\). Then \(x=\frac{1716}{39}=44\).

Answer:

\(44\)