Question

solve for x.
$x = \square$
(simplify your answer. type an integer or an improper fraction. use a comma to separate answers as needed.)

Explanation:

Step1: Identify triangle proportionality theorem

Since \(QT \parallel RS\) (marked by the parallel arrows), by the Triangle Proportionality Theorem (Basic Proportionality Theorem), the segments created on the sides of \(\triangle PQS\) are proportional:
$$\frac{PQ}{PT} = \frac{QR}{TS}$$

Step2: Substitute given values

Substitute \(PQ = x\), \(PT = 9\), \(QR = 4\), \(TS = 9\) into the proportion:
$$\frac{x}{9} = \frac{4}{9}$$

Step3: Solve for \(x\)

Multiply both sides by 9 to isolate \(x\):
$$x = \frac{4}{9} \times 9$$

Answer:

$4$