Question

△abc and △xyz are similar. find the missing side length.
(the triangles are not drawn to scale.)

Explanation:

Step1: Set up the proportion

Since the triangles are similar, the ratios of corresponding sides are equal. Let the missing side be \( x \). Then \(\frac{AB}{XY}=\frac{BC}{YZ}=\frac{AC}{XZ}\). Using \(\frac{AB}{XY}=\frac{AC}{XZ}\), we have \(\frac{8}{x}=\frac{20}{5}\).

Step2: Solve the proportion

Cross - multiply: \(20x = 8\times5\). So \(20x=40\). Divide both sides by 20: \(x=\frac{40}{20}\).

Answer:

\(2\)