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 sq and the perpendicular distance between the two parallel sides is 100 m , find the length of the side along the river

$Let\;the\;lenght\;of\;the\;side\;along\;road\;is\;x\;and\;length\;of\;the\;side\;along\;river\;is\;2x\\*Area \;of\;the\;field\;is\;10500\;m^2\\*perpendicular\;distance,(h)\;between\;two\;parallel\;sides\;is\;100\;m\\* Area\;of\;trapezium\;=\frac{1}{2}\times h\times (sum\; of\; two\; parallel\; sides)\\*\frac{1}{2}\times (100)\times (x+2x)=10500\\* 150\times x=10500\\*\Rightarrow x = \frac{10500}{150}\\* \Rightarrow x = 70\\*Hence,\;the\;length\;of\;the\;side\;along\;river\;is\;2\times x = 140\;m$

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