Question

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

Explanation:

Step1: Set up the proportion

Since $\triangle ABC$ and $\triangle ADE$ are similar, the ratios of their corresponding sides are equal. That is $\frac{CA}{EA}=\frac{BA}{DA}$. We know that $EA = 6$, $BA=2$, and $DA=2 + 2=4$. Let $CA=x$. So the proportion is $\frac{x}{6}=\frac{2}{4}$.

Step2: Cross - multiply and solve for x

Cross - multiplying gives us $4x=2\times6$. So $4x = 12$. Dividing both sides by 4, we get $x=\frac{12}{4}=3$.

Answer:

3