Mohan wants to buy a trapezium shaped field. Its side along the river is parallel to and twice the side along the road. If the area of this field is 10500 $m^2$ and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.

Let the side of the trapezium along the road be x cm.

And, The opposite parallel side = 2x m

Given, h = 100 m

Area = 10500 m²

Area of trapezium $= \frac{1}{2} (a + b) \times h$
$10500 = \frac{1}{2} (2x + x) \times 100$

$2 \times 10500 = 3x \times 100$

$21000 = 300x$

$x = 70 m$

So$, AB = 2x = 2 \times 70 = 140 m$

Hence, the required length = 140 m.