Question

$overline{qu} parallel overline{rt}$. find $qs$.
$qs = square$

Explanation:

Step1: Apply Basic Proportionality Theorem

Since $\overline{QU} \parallel \overline{RT}$, by the theorem, $\frac{SR}{RQ} = \frac{ST}{TU}$

Step2: Substitute known values

$\frac{20}{RQ} = \frac{26}{13}$
Simplify $\frac{26}{13}=2$, so $\frac{20}{RQ}=2$
Solve for $RQ$: $RQ = \frac{20}{2}=10$

Step3: Calculate length of QS

$QS = SR + RQ$
$QS = 20 + 10$

Answer:

30