Question

δabc and δade are similar. find the length of side ca

Explanation:

Step1: Set up proportion from similar triangles

Since $\triangle ABC$ and $\triangle ADE$ are similar, the ratios of corresponding sides are equal. So, $\frac{CA}{EA}=\frac{BA}{DA}$. We know $EA = 12$, $BA=4$, and $DA=4 + 8=12$.

Step2: Substitute values into proportion

Substituting the values into $\frac{CA}{12}=\frac{4}{12}$.

Step3: Solve for CA

Cross - multiply gives $12\times CA=4\times12$. Then $CA = 4$.

Answer:

4