Answer
$24.43\, inches$
Work Step by Step
The diagonals are 56 and 34 inches. The angle between them is either $120^{\circ}$ or $60^{\circ}$.
Now, the shorter side is opposite the shorter angle i.e. $60^{\circ}$
And the sides adjacent to $60^{\circ}$ are half the diagonals, i.e. 28 and 17 inches.
If we denote the shorter side by S, then
by laws of cosines, we have,
$S^{2}={28}^{2}+17^{2}-2(28)(17)(cos60^{\circ})$
Hence, $S = 24.43 \,inches$
