Question

triangle abc is similar to triangle def. find the measure of side fd. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Set up the proportion

Since \(\triangle ABC\sim\triangle DEF\), the ratios of corresponding sides are equal. That is \(\frac{AB}{DE}=\frac{AC}{DF}\). Let \(DF = x\). We know \(AB = 6\), \(DE=29\), and \(AC = 11.9\). So the proportion is \(\frac{6}{29}=\frac{11.9}{x}\).

Step2: Cross - multiply

Cross - multiplying gives us \(6x=29\times11.9\).
First, calculate \(29\times11.9 = 345.1\). So the equation becomes \(6x = 345.1\).

Step3: Solve for \(x\)

Divide both sides of the equation \(6x = 345.1\) by \(6\). \(x=\frac{345.1}{6}\).
\(x\approx57.5\)

Answer:

\(57.5\)