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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.