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.
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 m2 and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.
Solution
Let's solve the problem step by step:
Step 1: Let's assume the length of the side along the road is x meters. Step 2: According to the problem, the side along the river is twice the side along the road, so the length of the side along the river is 2x meters. Step 3: The area of a trapezium can be calculated using the formula: Area = (1/2) * (sum of parallel sides) * (perpendicular distance between them). Step 4: Substituting the given values, we have: 10500 = (1/2) * (x + 2x) * 100. Step 5: Simplifying the equation, we get: 10500 = (3x/2) * 100. Step 6: Dividing both sides of the equation by 100, we have: 105 = (3x/2). Step 7: Multiplying both sides of the equation by 2/3, we get: x = (105 * 2) / 3. Step 8: Simplifying the equation, we have: x = 70. Step 9: Therefore, the length of the side along the river is 2x = 2 * 70 = 140 meters.
So, the length of the side along the river is 140 meters.
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