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

1.	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» Given that, Let the length of side of trapezium shaped field along road = x meter Length of other side of trapezium shaped field along road = 2x meter Area of trapezium = 10500 cm² Distance between parallel sides = 100 m We know that, Area of trapezium = 1/2 (Sum of lengths of parallel sides) × distance between parallel sides i.e., Area of trapezium = 1/2 (Sum of sides) × distance between parallel sides 10500 = 1/2 (x + 2x) × 100 10500 = 1/2 (3x) × 100 3x = 10500/50 3x = 210 x = 210/3 = 70 x = 70 ∴ Length of side of trapezium shaped field along road = 70 m And, Length of other side of trapezium shaped field along road = 2x = 70× 2 = 140 m

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»

Given that,

Let the length of side of trapezium shaped field along road = x meter

Length of other side of trapezium shaped field along road = 2x meter

Area of trapezium = 10500 cm²

Distance between parallel sides = 100 m

We know that,

Area of trapezium = 1/2 (Sum of lengths of parallel sides) × distance between parallel sides

i.e., Area of trapezium = 1/2 (Sum of sides) × distance between parallel sides

10500 = 1/2 (x + 2x) × 100

10500 = 1/2 (3x) × 100

3x = 10500/50

3x = 210

x = 210/3 = 70

x = 70

∴ Length of side of trapezium shaped field along road = 70 m

And, Length of other side of trapezium shaped field along road = 2x = 70× 2 = 140 m