Question

solve for ( x ). figures are not necessarily drawn to scale.

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle DE F\) and \(\triangle GHF\) are similar. The ratio of corresponding sides is equal. That is \(\frac{x}{6}=\frac{2 + 4}{4}\).

Step2: Solve the proportion for \(x\)

Cross - multiply the proportion \(\frac{x}{6}=\frac{6}{4}\). We get \(4x=6\times6\). Then \(4x = 36\), and \(x=\frac{36}{4}=9\).

Answer:

\(x = 9\)