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 m² and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.

Answer 1

$$\begin{gathered} \text{Given:} \\ {\text{Area of the trapezium shaped field = 10500 m}}^2 \\ \text{It is also given that the length of the side along the river is double the length of the side along the road.} \\ \mathrm{Let}\mathrm{us}\mathrm{s}\text{uppose the length of the side along the road to be}x. \\ \text{Then, the length of the side along the river = 2×}x=2x \\ \text{And, the perpendicular distance between these parallel sides =100 m} \\ \text{Area of trapezium=}\frac{1}{2}\text{×(Sum of the parallel sides)×(Perpendicular distance)} \\ 10500=\frac{1}{2}\text{×(2x+x)×(100)} \\ \text{10500=50×(3x)} \\ \text{3x=}\frac{10500}{50}\text{=210} \\ \text{x=}\frac{210}{3}\text{=70 m} \\ \therefore \mathrm{L}\text{ength of the side along the river = 2×}x\text{= 2×70=140 m} \end{gathered}$$