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 10,500 m² and the
perpendicular distance between the two parallel sides is 100 m, find the length of the
side along the river.​

Answer 1

Answer:

Heya Here's your answer mate

Let the parallel sides of the trapezium-shaped field be ′x ′ m and ′2x ′ m.

Let a=x and b=2x and h=100m

Then, its area.

= 1 /2(a + b) x hm²

= 1 /2 (x + 2x) x 100 m²

=50 x 3x m² = 150x m²

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

Therefore, 150x = 10500

X = 10500 / 150 = 70 m

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

Thanks

have a great day ahead

Answer 2

Given :

• → Area of Trapezium shaped field (A) = 10,500m²
• → Height of Trapezium field (H) = 100 m

Need To Find :

• → Length of the side along the river.

Formula to be Used :

• → Area = 1/2 ( Sum of altitudes ) × Height

Assumptions Needed :

• → Let one side AD = x of other sides
• → BC = 2x
• → AE = H = 100

Putting value in Formula :

• → Area = 1/2 ( Sum of altitudes ) × Height
• → 10500 = 1/2 ( AD + BC ) × 100 m
• → 10500 = 1/2 ( x + 2x ) × 100 m
• → 10500/150 = x
• → x = 70

Hence :

Length of one side is x :

• → x = 70 m.

Length of second side is 2x :

• → 2x = 2 × 70 m = 140 m

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