Question

$\overline{rs} \parallel \overline{tv}$. find $tu$.
$st=11$, $vr=7$, the length of the segment parallel to $\overline{rs}$ on the other side is 21
$tu = \square$

Explanation:

Step1: Apply Triangle Proportionality Theorem

Since $\overline{RS} \parallel \overline{TV}$, the theorem gives $\frac{ST}{TU} = \frac{RV}{VU}$.

Step2: Substitute known values

$\frac{11}{TU} = \frac{7}{21}$

Step3: Simplify and solve for $TU$

First simplify $\frac{7}{21} = \frac{1}{3}$, so $\frac{11}{TU} = \frac{1}{3}$. Cross-multiply: $TU = 11 \times 3$

Answer:

33