Question

△abc and △ade are similar. find the length of side ca.

Explanation:

Step1: Set up proportion

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

Step2: Identify side - lengths

We know that $EA = 6$, $BA=2$, and $DA=2 + 4=6$.

Step3: Substitute values into proportion

Substituting the values into $\frac{CA}{EA}=\frac{BA}{DA}$, we get $\frac{CA}{6}=\frac{2}{6}$.

Step4: Solve for $CA$

Cross - multiply: $6\times CA=2\times6$. Then $CA = 2$.

Answer:

$2$