Weird Arrangement?!

Two congruent ellipses with the major axis $2a$ and the minor axis $\pi$ touch each other, the minor axis of each passing through the point of contact. $l$ is a common exterior tangent parallel to the minor axis. There are three congruent squares of side $t$ such that two of the squares have a side in common and another side lying on $l$ , and each has a vertex on one of the ellipses, and a third square has a vertex on each ellipse and a side that lies along a side of the first two squares.

Find the larger value of $\displaystyle \frac{5t}{a}$