Question

1. find x.

q 6 t 16

r
5 3 u x

\overline{tu} \parallel \overline{qs}

\bigcirc 6
\bigcirc 7
\bigcirc 8
\bigcirc 9

Explanation:

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

Since \( \overline{TU}\parallel\overline{QS}\), by the basic proportionality theorem in \(\triangle RQS\), we have \(\frac{RT}{TQ}=\frac{RU}{US}\).
Here, \(TQ = 6\), \(RT=16\), \(US = 3\). Let \(RU=x\).
The proportion becomes \(\frac{16}{6}=\frac{x}{3}\).

Step2: Solve the proportion for \(x\)

Cross - multiply: \(6x=16\times3\).
\(6x = 48\).
Divide both sides by 6: \(x=\frac{48}{6}\).

Answer:

\(8\)