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 $10500{\text{\hspace{0.17em}m}}^2$ and the perpendicular distance between the two parallel sides is $100\text{\hspace{0.17em}m}$, find the length of the side along the river.

Answer 1

Step1: Draw the diagram based on the given information.

The area of the field is $10500{\text{\hspace{0.17em}m}}^2$ and the perpendicular distance between the two parallel sides is $100\text{\hspace{0.17em}m}$.

Assume that the side along the road is $x\text{\hspace{0.17em}m}$.

So, the length of the side along the river is $2x\text{\hspace{0.17em}m}$.

Step 2: Calculate the length of the side along the river.

We know that the area of a trapezium is $\frac{1}{2}\left(\text{Sum\hspace{0.17em}of\hspace{0.17em}the\hspace{0.17em}length\hspace{0.17em}of\hspace{0.17em}parallel\hspace{0.17em}sides}\right)\times \left(\text{Perpendicular\hspace{0.17em}distance\hspace{0.17em}between\hspace{0.17em}parallel\hspace{0.17em}sides}\right)$

Therefore,

$\begin{array}{l}10500=\frac{1}{2}\times (x+2x)\times 100\\ \Rightarrow 10500=3x\times 50\\ \Rightarrow 10500=150x\\ \Rightarrow x=\frac{10500}{150}\text{\hspace{0.17em}m}\\ \Rightarrow x=70\text{\hspace{0.17em}m}\end{array}$

So, the length of the side along the river:

$\begin{array}{l}2\times 70\text{\hspace{0.17em}m}\\ =140\text{\hspace{0.17em}m}\end{array}$

Hence, the length of the side along the river is $140\text{m}$.