Question

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 $10500m^2$ and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.

Answer 1

Perpendicular distance (h) = 100 m
Area of the trapezium shaped field = $10500m^2$
Let side along the road be x m and side along the river = 2x m
Here , a = x m and b = 2x m
$\therefore$ Area of the trapezium field = $\frac{1}{2}(a+b)\times h$
$\Rightarrow 10500=\frac{1}{2}(x+2x)\times 100\Rightarrow 10500=3x\times 50$
$\Rightarrow 3x=\frac{10500}{50}\Rightarrow x=\frac{10500}{50\times 3}$
$\Rightarrow x=70m$
Hence the side along the river = $2x=2\times 70=140m$