Question

δabc and δade 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. That is $\frac{CA}{EA}=\frac{BA}{DA}$. We know $EA = 4$, $BA = 2$, and $DA=2 + 2=4$. Let $CA=x$. So we have $\frac{x}{4}=\frac{2}{4}$.

Step2: Solve for $x$

Cross - multiply the proportion $\frac{x}{4}=\frac{2}{4}$ to get $4x=4\times2$. Then $4x = 8$, and dividing both sides by 4 gives $x = 2$.

Answer:

2