Question

given lines l, m, and n are parallel..., your answer to the nearest tenth if necessary.
(image of parallel lines l, m, n cut by two transversals, with segments 24, 26, 9, and x labeled)

Explanation:

Step1: Apply the Basic Proportionality Theorem (Thales' theorem) for parallel lines.

Since lines \( l \), \( m \), and \( n \) are parallel, the segments created by the transversals are proportional. So we set up the proportion: \(\frac{24}{x}=\frac{26}{9}\)

Step2: Cross - multiply to solve for \( x \).

Cross - multiplying gives us \( 26x = 24\times9 \). First, calculate \( 24\times9=216 \). Then, solve for \( x \) by dividing both sides of the equation by 26: \( x=\frac{216}{26}\)

Step3: Simplify the fraction.

Simplify \(\frac{216}{26}\) by dividing 216 by 26. \( 216\div26\approx8.3\) (rounded to the nearest tenth)

Answer:

\( 8.3 \)