Question

given \\( \triangle a b c sim \triangle d e f \\), choose the proportion that is set up incorrectly.
\\( \frac{x}{25}=\frac{28}{20} \\)
\\( \frac{20}{28}=\frac{25}{x} \\)
\\( \frac{x}{20}=\frac{28}{25} \\)
\\( \frac{25}{x}=\frac{20}{28} \\)

Explanation:

Step1: Recall the property of similar triangles

For similar triangles \(\triangle ABC\sim\triangle DEF\), the ratios of corresponding sides are equal. That is \(\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}\). Here \(AB = x\), \(BC = 28\), \(DE = 25\), \(EF=20\).

Step2: Check each proportion

• For \(\frac{x}{25}=\frac{28}{20}\): Cross - multiply gives \(20x=25\times28\). Since \(AB\) corresponds to \(DE\) and \(BC\) corresponds to \(EF\), this proportion is correct.
• For \(\frac{20}{28}=\frac{25}{x}\): Cross - multiply gives \(20x = 28\times25\). But \(EF = 20\) corresponds to \(BC = 28\) and \(DE=25\) corresponds to \(AB=x\), so \(\frac{EF}{BC}=\frac{DE}{AB}\) is correct.
• For \(\frac{x}{20}=\frac{28}{25}\): Cross - multiply gives \(25x=20\times28\). But \(AB=x\) should correspond to \(DE = 25\) and \(BC = 28\) should correspond to \(EF = 20\). The correct proportion should be \(\frac{x}{25}=\frac{28}{20}\), so this proportion is incorrect.
• For \(\frac{25}{x}=\frac{20}{28}\): Cross - multiply gives \(20x=25\times28\). Since \(DE = 25\) corresponds to \(AB=x\) and \(EF = 20\) corresponds to \(BC = 28\), this proportion is correct.

Answer:

\(\frac{x}{20}=\frac{28}{25}\)