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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.

Answer :

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.