Question

triangle abc is similar to triangle abc. if ab is 12, what is the length of ab? type your answer in the box. ab =

Explanation:

Step1: Find the similarity ratio

Since \(\triangle ABC\sim\triangle A'B'C\), the similarity ratio \(k\) can be found by \(\frac{BB' + B'C}{B'C}=\frac{3 + 6}{6}=\frac{9}{6}=\frac{3}{2}\) (using the side - length relationship of similar triangles). Another way is to use the ratio of corresponding sides. Let \(AB = 12\), and assume the ratio of \(AB\) to \(A'B'\) is the same as the ratio of \(BC\) to \(B'C\). The length of \(BC=3 + 6=9\) and \(B'C = 6\).

Step2: Set up the proportion

We know that for similar triangles \(\frac{AB}{A'B'}=\frac{BC}{B'C}\). Substitute \(AB = 12\), \(BC = 9\), and \(B'C=6\) into the proportion \(\frac{12}{A'B'}=\frac{9}{6}\). Cross - multiply gives \(9\times A'B'=12\times6\).

Step3: Solve for \(A'B'\)

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Answer:

\(8\)