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 $100m$, find the length of the side along the river.

• A. $140m$
• B. $240m$
• C. $140cm$
• D. None of these

Answer 1

The correct option is A $140m$

Let the parallel sides of the trapezium-shaped field be ${}^{\prime }{x}^{\prime }mand{}^{\prime }2x^{\prime }m$.

Let $a=x$ and $b=2x$ and $h=100m$

Then, its area.

$=\frac{1}{2}(a+b)\times h{m}^2$

$=\frac{1}{2}(x+2x)\times 100m^2$

$=50\times 3x{m}^2=150x{m}^2$

But it is given that the area of the field is $10500m^2$

$\therefore 150x=10500$

$\Rightarrow x=\frac{10500}{150}=70$

$\therefore$ The length of the side along the river is $2\times 70$, i.e., $140m$.