Question

1 △abc-△def

Explanation:

Step1: Use the property of similar triangles

For similar triangles \(\triangle ABC\) and \(\triangle DEF\), the ratios of corresponding sides are equal. That is \(\frac{AB}{DE}=\frac{AC}{DF}\). Here \(AB = 6\), \(DF=3\), \(AC = 4\), and \(DE=x\).

Step2: Set up the proportion

We have the proportion \(\frac{6}{x}=\frac{4}{3}\).

Step3: Cross - multiply

Cross - multiplying gives \(4x=6\times3\).

Step4: Solve for \(x\)

\(4x = 18\), then \(x=\frac{18}{4}=\frac{9}{2}=4.5\).

Answer:

\(x = 4.5\)