Question

△abc and △def are similar. find the missing side length.

(the triangles are not drawn to scale.)

Explanation:

Step1: Find the scale factor

Since \(\triangle ABC \sim \triangle DEF\), the ratio of corresponding sides is equal. Let's take sides \(AB\) and \(DE\). \(AB = 5\), \(DE = 35\). The scale factor \(k=\frac{AB}{DE}=\frac{5}{35}=\frac{1}{7}\). Alternatively, check with \(AC\) and \(DF\): \(AC = 7\), \(DF = 49\), \(\frac{7}{49}=\frac{1}{7}\), so scale factor is \(\frac{1}{7}\) (or we can say \(\triangle ABC\) is smaller by scale factor \(\frac{1}{7}\) compared to \(\triangle DEF\)).

Step2: Find the missing side

The side \(EF = 56\) in \(\triangle DEF\), corresponding side in \(\triangle ABC\) is the missing side (let's call it \(BC\)). Using the scale factor, \(BC = EF\times\frac{1}{7}\). Substitute \(EF = 56\), so \(BC = 56\times\frac{1}{7}=8\).

Answer:

\(8\)