Question

△abc and △pqr 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 \(x\). We have the proportion \(\frac{AB}{PQ}=\frac{AC}{PR}\). Substituting the values: \(\frac{2}{12}=\frac{4}{x}\).

Step2: Cross - multiply

Cross - multiplying gives \(2x = 12\times4\).

Step3: Solve for \(x\)

First, calculate \(12\times4 = 48\). Then, \(2x=48\), so \(x=\frac{48}{2}=24\).

Answer:

\(24\)