Question

Shyam wants to buy a trapezium shaped field in between a road and a river. Its side along the river is parallel to 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.

• A. 140 m
• B. 70 m
• C. 100 m
• D. 180 m

Answer 1

The correct option is A 140 m

Let the side of the trapezium (roadside) be $x$ cm.
The opposite parallel river side $=2xm$
$h=100m$
$Area=10500m^2$
$Areaoftrapezium=\frac{1}{2}(2x+x)\times 100$
$10500=\frac{1}{2}(2x+x)\times 100$
$2\times 10500=3x\times 100$
$21000=300x$
$x=70m$
So, $riverside=2x=2\times 70=140m$
Hence, the required length is 140 m.