Question

question 3
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)

Since lines \( l\), \(m\), and \(n\) are parallel and cut by two transversal lines, we can use the proportion \(\frac{21}{x}=\frac{16}{13}\).

Step2: Solve the proportion for \(x\)

Cross - multiply the proportion \(\frac{21}{x}=\frac{16}{13}\) to get \(16x = 21\times13\). Then \(16x=273\). Divide both sides by 16: \(x=\frac{273}{16}\).

Step3: Calculate the value of \(x\)

\(x=\frac{273}{16}=17.0625\approx17.1\)

Answer:

\(17.1\)