Question

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

Explanation:

Step1: Find the scale factor

Since \(\triangle ABC\sim\triangle PQR\), the ratio of corresponding sides is equal. Consider the sides \(AB = 32\) and \(PQ=4\). The scale factor \(k=\frac{PQ}{AB}=\frac{4}{32}=\frac{1}{8}\)

Step2: Calculate the missing side

The side \(AC = 56\) corresponds to \(PR\). Let \(PR=x\). Using the proportion \(\frac{PR}{AC}=\frac{PQ}{AB}\), substitute the values: \(\frac{x}{56}=\frac{4}{32}\)
Cross - multiply: \(32x = 4\times56\)
\(32x=224\)
Solve for \(x\): \(x=\frac{224}{32}=7\)

Answer:

\(7\)