Question

midterm (chapters 4, 5, 6, 8.1, 8.2) question 47, 8.2.54 hw score: 95.74%, 45 of 47 points points: 0 of 1 △abc and △ade are similar. find the length of side $overline{ca}$

Explanation:

Step1: Set up proportion from similarity

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

Step2: Identify side - lengths

From the figure, $EA = 12$, $BA = 4$, and assume $DA$ is the sum of the two - segment lengths on the side $DA$. Let's assume the full length of $DA$ is $8$ (if the non - labeled part from $B$ to $D$ is $4$ as well).

Step3: Substitute values into proportion

Substituting into $\frac{x}{12}=\frac{4}{8}$.

Step4: Cross - multiply and solve

Cross - multiplying gives $8x=4\times12$, so $8x = 48$. Then $x=\frac{48}{8}=6$.

Answer:

$6$