Question

solve for x. the triangles are similar. 1 64 8 56 7 x - 1 80

Explanation:

Step1: Find the ratio of corresponding sides

Since the triangles are similar, the ratio of corresponding sides is equal. The ratio of \(DK\) to \(DE\) is \(\frac{8}{64}=\frac{1}{8}\).

Step2: Set up the proportion for the sides of the triangles

Let \(\triangle DKJ\) and \(\triangle DEF\) be the similar triangles. Then \(\frac{DK}{DE}=\frac{DJ}{DF}\). We know \(DK = 8\), \(DE=64\), \(DJ=x - 1\), and \(DF = 80\). Substituting the values into the proportion: \(\frac{8}{64}=\frac{x - 1}{80}\).

Step3: Solve the proportion for \(x\)

Cross - multiply: \(8\times80=64\times(x - 1)\).

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Answer:

\(x = 11\)