Question

δabc and δade are similar. find the length of side (overline{ca}).

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle ABC\) and \(\triangle ADE\) are similar, the ratios of their corresponding sides are equal. That is \(\frac{CA}{EA}=\frac{BC}{DE}\).

Step2: Substitute the known values

We know that \(BC = 5\), \(DE=10\), and \(EA = 12\). Let \(CA=x\). Substituting into the proportion \(\frac{x}{12}=\frac{5}{10}\).

Step3: Solve the proportion for \(x\)

Cross - multiply: \(10x=5\times12\). Then \(10x = 60\). Divide both sides by 10: \(x=\frac{60}{10}=6\).

Answer:

The length of side \(\overline{CA}\) is \(6\).