Question 120
Let $n$ be the answer to this problem. Suppose square $ABCD$ has side-length $3$. Then, congruent non-overlapping squares $EHGF$ and $IHJK$ of side-length $\frac{n}{6}$ are drawn such that $A$, $C$, and $H$ are collinear, $E$ lies on $BC$ and $I$ lies on $CD$. Given that $AJG$ is an equilateral triangle, then the area of $AJG$ is $a + b \sqrt{c}$, where $a$, $b$, $c$ are positive integers and $c$ is not divisible by the square of any prime. Find $a + b + c$.
Proposed by: Akash Das
Proposed by: Akash Das