Question

the two triangles are similar. solve for de.

Explanation:

Step1: Use the property of similar triangles

Since the two triangles are similar, the ratios of their corresponding sides are equal. That is \(\frac{AB}{DE}=\frac{BC}{EF}\).

Step2: Substitute the known values

Let \(AB = 18\), \(BC=9\), \(EF = 2\). Then \(\frac{18}{DE}=\frac{9}{2}\).

Step3: Cross - multiply

Cross - multiplying gives \(9\times DE=18\times2\).

Step4: Solve for \(DE\)

\(9DE = 36\), so \(DE=\frac{36}{9}=4\).

Answer:

\(4\)