HMMT 2008 U21

Let $A B C$ be a triangle with $A B=5, B C=4$ and $A C=3$. Let $\mathcal{P}$ and $\mathcal{Q}$ be squares inside $A B C$ with disjoint interiors such that they both have one side lying on $A B$. Also, the two squares each have an edge lying on a common line perpendicular to $A B$, and $\mathcal{P}$ has one vertex on $A C$ and $\mathcal{Q}$ has one vertex on $B C$. Determine the minimum value of the sum of the areas of the two squares.