Question

st || uw. find tu. tu =

Explanation:

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

Since \( \overline{ST}\parallel\overline{UW}\), we have the proportion \(\frac{TU}{TV}=\frac{SW}{SV}\). Let \(TU = x\), then \(TV=x + 33\), \(SW = 48\), and \(SV=48 + 72=120\). So the proportion becomes \(\frac{x}{x + 33}=\frac{48}{120}\).

Step2: Cross - multiply

Cross - multiplying gives \(120x=48(x + 33)\).

Step3: Expand the right - hand side

Expanding \(48(x + 33)\) gives \(120x=48x+1584\).

Step4: Solve for \(x\)

Subtract \(48x\) from both sides: \(120x-48x=1584\), so \(72x = 1584\). Then \(x=\frac{1584}{72}=22\).

Answer:

\(22\)