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

Since \( l\parallel m\parallel n\), by the basic proportionality theorem (also known as the Thales' theorem for parallel lines intersected by transversals), we have the proportion \(\frac{16}{x}=\frac{23}{38}\).

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

Cross - multiplying gives us \(23x = 16\times38\).
First, calculate \(16\times38=608\). So, \(23x = 608\).
Then, \(x=\frac{608}{23}\).

Step3: Calculate the value of \(x\)

\(x=\frac{608}{23}\approx26.4\)

Answer:

\(x\approx26.4\)