Question

△abc ~ △def. find the values of x and y.

Explanation:

Step1: Set up the proportion for corresponding sides

Since $\triangle ABC\sim\triangle DEF$, the ratios of corresponding sides are equal. For the sides $BC$ and $EF$, and $AB$ and $DF$, we have $\frac{BC}{EF}=\frac{AB}{DF}=\frac{AC}{DE}$. So, $\frac{4}{12}=\frac{8}{y}=\frac{12}{x}$.

Step2: Solve for $y$

From $\frac{4}{12}=\frac{8}{y}$, we cross - multiply: $4y = 8\times12$. Then $4y=96$, and $y=\frac{96}{4}=24$.

Step3: Solve for $x$

From $\frac{4}{12}=\frac{12}{x}$, we cross - multiply: $4x = 12\times12$. Then $4x = 144$, and $x=\frac{144}{4}=36$.

Answer:

$x = 36$, $y = 24$