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# 8.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 100m, find the length of the side along the river.

Given, area of trapezium field area=10500$$m^2$$, Altitude of the field(h)=100m.
Let, the side of the trapezium near road be x cm and the opposite parallel side = 2x m

We know, area of trapezium = $$\frac { 1 }{ 2 }\times (a + b) \times h$$

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

$$\Rightarrow 2 \times10500 = 3x \times 100$$

$$\Rightarrow 21000 = 300x$$

$$\Rightarrow x = 70 m$$

So, the other side = $$2x = 2 \times 70 = 140 m$$

Hence, the required length of the side along the river= 140 m.