The problem asks to identify which of the given ratios are equivalent to the ratio $6:12$. The ratios to consider are $4:10$, $5:11$, $1:2$, $18:36$, and $24:48$.

1. Problem Description

The problem asks to identify which of the given ratios are equivalent to the ratio $6:12$. The ratios to consider are $4:10$, $5:11$, $1:2$, $18:36$, and $24:48$.

2. Solution Steps

A ratio $a:b$ is equivalent to $6:12$ if $\frac{a}{b} = \frac{6}{12}$. Simplify the ratio $6:12$ to its simplest form.

$\frac{6}{12} = \frac{1}{2}$

Therefore, we are looking for ratios that are equivalent to $1:2$.

Now, consider each option:

* $4:10$. $\frac{4}{10} = \frac{2}{5}$. Since $\frac{2}{5} \neq \frac{1}{2}$, $4:10$ is not equivalent to $6:12$.

* $5:11$. $\frac{5}{11} \neq \frac{1}{2}$, so $5:11$ is not equivalent to $6:12$.

* $1:2$. $\frac{1}{2} = \frac{1}{2}$, so $1:2$ is equivalent to $6:12$.

* $18:36$. $\frac{18}{36} = \frac{1}{2}$, so $18:36$ is equivalent to $6:12$.

* $24:48$. $\frac{24}{48} = \frac{1}{2}$, so $24:48$ is equivalent to $6:12$.

3. Final Answer

The ratios equivalent to $6:12$ are $1:2$, $18:36$, and $24:48$.