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

Answer 1

$\large \bf {\pink {✰Question࿐}}$

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 $\sf 10,500m^2$, and the perpendicular distance between the two parallel sides is $\sf 100m$, find the length of the side along the river.

$\large \bf \pink {✰Solution࿐}$

Given that :-

• Area of trapezium = $\sf 10,500m^2$
• Height (Distance of perpendicular between parallel sides) = $\sf 100m$
• Side along river = Twice side along road

Let side along road be x.

Side along river = 2x.

$\underline {\boxed {\mathfrak \orange {Area \: of \: trapezium= \frac{1}{2} \times (Sum \: of \: parallel \: sides) \times Height}}}$

Substituting and solving :-

$\orange{ : \:☞}\:\sf 10500 = \cfrac{1}{2} \times (x + 2x) \times 100$

$\orange {: \: ☞}\:\sf 10500= \cfrac{1}{\cancel2} \times (3x )\times (\cancel{100})$

$\orange{ : \: ☞}~\sf 10500=3x(50)$

$\orange {: \: ☞}\sf 10500=150x$

$\orange {: \: ☞} \: \sf \cancel \cfrac {10500}{150} =x$

$\orange {: \: ☞}\:\sf x=70m$

$\large \underline{\boxed {\mathfrak \orange {\therefore Side \: along \: the \: road = x = 70m}} }$

$\large \underline {\boxed {\mathfrak \orange {\therefore Side \: along \: the \: river = 2x = 140m} }}$

$\large \bf \pink {✰Additional \: info࿐}$

$\orange {:~☞}\:\sf Area_{(rectangle)}=Length \times Breadth$

$\orange {:~☞}~\sf Area_{(square)}=Side \times Side$

$\orange {:~☞}~\sf Area_{(parallelogram)}=Base \times Height$

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Answer 2

Let the parallel sides of the trapezium-shaped field be ′ x ′

m and ′2x ′m.

$\bold\pink{Let \: a \: = \: x \: and \: b \: = \: 2x \: and \: h \: = \: 100m}$

Then, its area.

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

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

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

But it is given that the area of the field is 10500 m²

∴150x = 10500

$\bold{⇒x = \frac{10500}{150} = 70}$

∴ The length of the side along the river is 2 × 70, i.e., 140m.