Vector Algebra

A parallelogram is constructed on $5\bar{a} + 2\bar{b}$ and $\bar{a} - 3\bar{b}$ as its adjacent sides, with $|\bar{a}| = 2\sqrt{2}, |\bar{b}| = 3$ . The angle between $\bar{a}$ and $\bar{b}$ is $\dfrac{\pi}{4}$ . Then the length of the diagonals of the parallelogram are