Question

Avinash 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 21000 m sq. and the perpendicular distance between the two
parallel sides is 200 m, find the length of the side along the river.

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Answer 1

Given:

• Side toward river is twice the side toward road.
• Area of trapezium is 21000m²
• perpendicular distance (height) is 200m

To find :

• Length of side toward river ?

Solution:

As given in question that,side along the river is twice the side along the road.

Let suppose that side toward road is x therefore, side toward river will be 2x.

• Side of trapezium toward road = x
• Side of trapezium toward river = 2x

Now, given that area of trapezium is 21000m² and height is 200m where we have supposed two parallel sides are x and 2x respectively.

We know that :

• $\large{\boxed{\sf{\pink{Area\:of\: parallelogram\:=\: \dfrac{b_{1} + b_{2}}{2}×h}}}}$

Where,

• $\small{\sf{ b_{1}\:=\: 1st ~base}}$
• $\small{\sf{ b_{2}\:=\: 2nd~ base}}$
• h = height ( perpendicular distance)

Let put known value in formula :-

$\large{\sf{Area\:of\: parallelogram\:=\: \dfrac{b_{1} + b_{2}}{2}×h}}$

$\implies\large\sf{21000\:=\: \dfrac{x+2x}{2}×200}$

$\implies\large\sf{21000\:=\: \dfrac{3x}{2}×200}$

$\implies\large\sf{21000\:=\: \dfrac{3x}{\cancel{2}}×\cancel{200}}$

$\implies\large\sf{21000\:=\: 3x ×100}$

$\implies\large\sf{3x\:=\: \dfrac{21000}{100}}$

$\implies\large\sf{3x\:=\:{\cancel\dfrac{21000}{100}}}$

$\implies\large\sf{3x\:=\:210}$

$\implies\large\sf{x\:=\:\dfrac{210}{3}}$

$\implies\large\sf{x\:=\:{\cancel\dfrac{210}{3}}}$

$\implies\large\sf{x\:=\: 70}$

Therefore,

• side of trapezium toward is 70m

As we have discussed and as per given condition, side of trapezium toward river is twice the side of trapezium toward road.

Hence,

• Length of side toward river = 2 × 70 = 140m