Mohan wants to buy a trapezium shaped field.

Given:

Area of the trapezium shaped field $=10500 \mathrm{~m}^{2}$

It is also given that the length of the side along the river is double the length of the side along the road.

Let us suppose the length of the side along the road to be $x .$

Then, the length of the side along the river $=2 \times x=2 x$

And, the perpendicular distance between these parallel sides $=100 \mathrm{~m}$

Area of trapezium $=\frac{1}{2} \times($ Sum of the parallel sides $) \times($ Perpendicular distance $)$

$10500=\frac{1}{2} \times(2 \mathrm{x}+\mathrm{x}) \times(100)$

$10500=50 \times(3 \mathrm{x})$

$3 \mathrm{x}=\frac{10500}{50}=210$

$\mathrm{x}=\frac{210}{3}=70 \mathrm{~m}$

$\therefore$ Length of the side along the river $=2 \times x=2 \times 70=140 \mathrm{~m}$