Question

given lines l, m, and n are parallel and cut by two transversal lines, find the value of x. round your answer to the nearest tenth if necessary.

Explanation:

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

When three parallel lines are cut by two transversals, the segments are proportional. So we set up the proportion: $\frac{9}{x}=\frac{38}{44}$.

Step2: Solve for \( x \) by cross - multiplying.

Cross - multiplying gives us \( 38x = 9\times44 \). First, calculate \( 9\times44 = 396 \). Then, \( x=\frac{396}{38}\approx10.4 \) (rounded to the nearest tenth).

Answer:

\( x\approx10.4 \)