Question

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

Explanation:

Step1: Identify corresponding sides

Since $\triangle ABC$ and $\triangle ADE$ are similar, the ratios of their corresponding sides are equal. The ratio of $AD$ to $AB$ is the same as the ratio of $AE$ to $AC$. We know $AD=2 + 2=4$, $AB = 2$, and $AE = 4$.

Step2: Set up proportion

Let $CA=x$. The proportion is $\frac{AD}{AB}=\frac{AE}{AC}$, substituting values we get $\frac{4}{2}=\frac{4}{x}$.

Step3: Solve for $x$

Cross - multiply: $4x=2\times4$. Then $4x = 8$, and $x = 2$.

Answer:

$2$