Question

8. 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 m² and the perpendicular distance
between the two parallel sides is 100 m, find the
length of the side along the river.
Top surface of a raised platform is in the shape
ofthe octagonalourfa

Answer 1

The length of the side along the river is 140 m

Explanation:

Equations

To solve the problem, we need to recall the area of a trapezium is:

`\displaystyle A=(b1+b2)/(2).h`

Where b1 and b2 are the lengths of the parallel sides and h is the height of the trapezium.

The field to be bought by Mohan has a trapezium shape with a side along the road of side x and a side along the river of side 2x, as stated in the problem.

Knowing the height is h=100 m, and the area is 10500 m2:

`\displaystyle (x+2x)/(2)\cdot 100=10500`

Simplifying:

`\displaystyle (3x)\cdot 50=10500`

`150x=10500`

Dividing by 150:

`x = 10500 / 150 = 70`

x = 70 m

2x = 140 m

The length of the side along the river is 140 m