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.See answer

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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 m and the perpendicular distance between the…

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.

Basic Answer

Step 1: Define Variables

Let the length of the side along the road be $x$ meters.

Step 2: Express the Length of the Side Along the River

Since the side along the river is twice the side along the road, the length of the side along the river is $2x$ meters.

Step 3: Use the Area Formula for a Trapezium

The area $A$ of a trapezium is given by:
$$A=\frac{1}{2}\times \text{(sum of parallel sides)}\times \text{(perpendicular distance)}$$

Given:

• Area $A=10500$ m²
• Perpendicular distance between the parallel sides = 100 m

Substitute the known values into the formula:
$$10500=\frac{1}{2}\times (x+2x)\times 100$$

Step 4: Simplify the Equation

$$10500=\frac{1}{2}\times 3x\times 100$$
$$10500=150x$$

Step 5: Solve for $x$

$$x=\frac{10500}{150}$$
$$x=70$$

Step 6: Find the Length of the Side Along the River

The length of the side along the river is $2x$:
$$2x=2\times 70=140$$

Final Answer

The length of the side along the river is $140$ meters.