question_answer 1)

                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 \[10,500\,{{m}^{2}}\] and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.

Answer:

                Let the length of the side along the river be \[2x\,\,m\]. Then, the length of the side along the road is \[x\,\,m\]. Area of the field = 10,500 square metres \[\Rightarrow \]               \[\frac{(2x+x)\times 100}{2}=10,\,500\] \[\Rightarrow \]               \[150x=10,\,500\] \[\Rightarrow \]               \[x=\frac{10,\,500}{150}\] \[\Rightarrow \]               \[x=70\] \[\Rightarrow \]               \[2x=2\times 70=140\,m\] Hence, the length of the side along the river is 140 m.