Question

in the diagram below, \\( \overline{st} \\) is parallel to \\( \overline{pq} \\). \\( rt = 20 \\), \\( sp = 18 \\), and \\( tq = 12 \\). find the length of \\( \overline{rs} \\). round your answer to the nearest tenth if necessary.

Explanation:

Step1: Apply Triangle Proportionality Theorem

Since $\overline{ST} \parallel \overline{PQ}$, the theorem gives $\frac{RS}{SP} = \frac{RT}{TQ}$

Step2: Substitute given values

Substitute $SP=18$, $RT=20$, $TQ=12$:
$\frac{RS}{18} = \frac{20}{12}$

Step3: Solve for $RS$

Multiply both sides by 18:
$RS = 18 \times \frac{20}{12}$
Simplify $\frac{20}{12}=\frac{5}{3}$, so $RS = 18 \times \frac{5}{3} = 30$

Answer:

30