A field is in the form of a trapezium.

Let the length of the required side be $x \mathrm{~cm}$.

Now,

Area of trapezium $=\left\{\frac{1}{2} \times(84+x) \times 26\right\} \mathrm{m}^{2}$

$=(1092+13 x) \mathrm{m}^{2}$

Area of trapezium $=1586 \mathrm{~m}^{2}$ (Given)

$\therefore 1092+13 x=1586$

$\Rightarrow 13 x=(1586-1092)$

$\Rightarrow 13 x=494$

$\Rightarrow x=\frac{494}{13}$

$\Rightarrow x=38 \mathrm{~m}$

Hence, the length of the other side is $38 \mathrm{~m}$