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

Answer 1

Answer:

70m

Step-by-step explanation:

area = 1/2 * sum of // sides * height

10500= 1/2 *( x + 2x)* 100

10500/50= 3x

210/3=x

x=70m

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Answer 2

$\large\underline{\bold{Given \:Question - }}$

• 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 sq. meter and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.

$\large\underline{\bold{ANSWER-}}$

Given :-

• A trapezium field whose side along the river is parallel to and twice the side along the road.

• Area of this trapezium field is 10500 square meter.

• The perpendicular distance between the two parallel sides is 100m,

To find :-

• The length of the side along the river.

Formula Used :-

$\sf \: Area_{(trapezium)} = \dfrac{1}{2} (sum \: of \parallel \: sides) \times distance \: between \: them$

$\large\underline{\bold{Solution-}}$

Given that

• A trapezium field whose side along the river is parallel to and twice the side along the road.

So,

• Let the side of field along the road be 'x' meter.

So,

• The side of the field along the river be '2x' meter.

Also,

• The perpendicular distance between the two parallel sides is 100m,

• Let perpendicular distance is represented by 'h'.

So,

• h = 100 m

Also,

• Area of this trapezium field = 10500 square meter.

So,

Using formula for area of trapezium, we get

$\rm :\longmapsto\:\sf \: Area_{(trapezium)} = \dfrac{1}{2} (sum \: of \parallel \: sides) \times h$

$\rm :\longmapsto\:10500 = \dfrac{1}{2} (x + 2x) \times 100$

$\rm :\longmapsto\:3x = 210$

$\rm :\implies\:x \: = \: 70 \: m$

Hence,

The side of the field along the river = 2x = 2 × 70 = 140 m.

Additional Information :-

Trapezium

• A trapezium is a quadrilateral, which is defined as a shape with four sides and one set of parallel sides

Properties of trapezium :-

• The sum of all the four angles of the trapezium is equal to 360°

• A trapezium has two parallel sides and two non-parallel sides

• The diagonals of regular trapezium bisect each other

• The length of the mid-segment is equal to half the sum of the parallel bases, in a trapezium

• Two pairs of adjacent angles of a trapezium formed between the parallel sides and one of the non-parallel side, add to 180 degrees