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 of one transversal are proportional to the corresponding segments of the other transversal. So, we have the proportion: $\frac{13}{38}=\frac{x}{37}$

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

Cross - multiplying gives us \( 38x = 13\times37 \). First, calculate \( 13\times37=481 \). Then, \( x=\frac{481}{38}\approx12.66 \)

Step3: Round to the nearest tenth.

Rounding \( 12.66 \) to the nearest tenth, we look at the hundredth place (6). Since \( 6\geq5 \), we round up the tenth place. So \( x\approx12.7 \)

Answer:

\( 12.7 \)