#### Question

Mohan wants to buy a trapezium shaped field. Its side along the river is parallel 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.

#### Solution

Given:

Area of the trapezium shaped field = 10500 m^{2}

It is also given that the length of the side along the river is double the length of the side along the road.

Let us suppose the length of the side along the road to be x.

Then, the length of the side along the river =\[ 2\times x = 2x\]

And, the perpendicular distance between these parallel sides =100 m

Area of trapezium \[=\frac{1}{2}\times(\text{ Sum of the parallel sides })\times(\text{ Perpendicular distance })\]

\[10500 = \frac{1}{2}\times(2x+x)\times(100)\]

\[10500=50\times(3x)\]

\[3x=\frac{10500}{50}=210\]

\[x=\frac{210}{3}=70 m\]

\[ \therefore\text{ Length of the side along the river }= 2\times x= 2\times70=140 m\]