Question

triangle cde is similar to triangle fgh. find hf. round your answer to the nearest tenth if necessary. figures are not drawn to scale.

(image of triangle cde with ce=19, ed=9; image of triangle fgh with hg=34, hf=x)

Explanation:

Step1: Identify Corresponding Sides

Since \(\triangle CDE \sim \triangle FGH\), corresponding sides are proportional. So, \(\frac{CE}{HF}=\frac{DE}{GH}\). Here, \(CE = 19\), \(DE = 9\), \(GH = 34\), and \(HF = x\).

Step2: Set Up Proportion

Substitute the values into the proportion: \(\frac{19}{x}=\frac{9}{34}\).

Step3: Solve for \(x\)

Cross - multiply: \(9x=19\times34\). Calculate \(19\times34 = 646\). Then \(x=\frac{646}{9}\approx71.8\).

Answer:

\(71.8\)