Let $ABCD$ be a square of side length $1$, and let $E$ and $F$ be points on $BC$ and $DC$ such that $\angle{EAF}=30^\circ$ and $CE=CF$. Determine the length of $BD$.

[i]2015 CCA Math Bonanza Lightning Round #4.2[/i]
1. **Understanding the problem**: We are given a square \(ABCD\) with side length 1. Points \(E\) and \(F\) are on sides \(BC\) and \(DC\) respectively, such that \(\angle EAF = 30^\circ\) and \(CE = CF\). We need to determine the length of the diagonal \(BD\).

2. **Analyzing the square**: In a square, the diagonals are equal in length and they bisect each other at right angles. The length of the diagonal of a square with side length \(s\) is given by:
   \[
   \text{Diagonal} = s\sqrt{2}
   \]
   Here, \(s = 1\), so the length of the diagonal \(BD\) is:
   \[
   BD = 1\sqrt{2} = \sqrt{2}
   \]

3. **Considering the additional information**: The problem mentions points \(E\) and \(F\) and the angle \(\angle EAF = 30^\circ\). However, this information is not necessary to determine the length of the diagonal \(BD\) of the square. The length of the diagonal is solely dependent on the side length of the square.

4. **Conclusion**: The length of the diagonal \(BD\) of the square \(ABCD\) with side length 1 is \(\sqrt{2}\).

The final answer is \(\boxed{\sqrt{2}}\).