8. In a planar convex quadrilateral with an area of 32 square centimeters, the sum of the lengths of one pair of opposite sides and one diagonal is $16 \mathrm{~cm}$. Determine all possible lengths of this diagonal.


8. Establish a coordinate system, set $A(-a, 0), B\left(b,-b^{\prime}\right), C(c, 0), D(0, d)$, then $S_{A B C D}=$
$$
\begin{array}{l}
\frac{1}{2}(c+a) d+\frac{1}{2}(c+a) d^{\prime}=32,|A B|+|C D|+|A C|=\sqrt{(a+b)^{2}+b^{\prime 2}}+ \\
\sqrt{c^{2}+d^{2}}+(a+c)=16 .
\end{array}
$$

Since $b^{\prime}+d \leqslant \sqrt{(a+b)^{2}+b^{\prime 2}}+\sqrt{c^{2}+d^{2}}$, we have $[(a+c)-8]^{2} \leqslant 0$, thus $a+$ $c=8$. Therefore, the length of the other diagonal $|B D|=8 \sqrt{2}$ cm.