Question

m.12 triangle proportionality theorem 6wa
find qs.
$qs = \square$
(the triangle has side lengths: tp = 26, pq = 13, qr = 9, with ts parallel to pr)

Explanation:

Step1: Apply Triangle Proportionality Theorem

Since $TS \parallel PR$, $\frac{TP}{PQ} = \frac{SR}{RQ}$

Step2: Substitute known values

$\frac{26}{13} = \frac{SR}{9}$

Step3: Solve for $SR$

$SR = \frac{26}{13} \times 9 = 2 \times 9 = 18$

Step4: Calculate total length $QS$

$QS = SR + RQ = 18 + 9$

Answer:

27