Answer:
To find the length of the side along the river in the trapezium-shaped field Mohan wants to buy, we can use the formula for the area of a trapezium:
\[ \text{Area} = \frac{1}{2} \times (\text{a} + \text{b}) \times h \]
where:
- \(\text{Area}\) is the area of the trapezium,
- \(\text{a}\) and \(\text{b}\) are the lengths of the two parallel sides,
- \(h\) is the height (or the perpendicular distance between the two parallel sides).
Given:
- The area of the field is \(10500 \, m^2\),
- The perpendicular distance (\(h\)) between the two parallel sides is \(100 \, m\),
- The side along the river is twice the side along the road, so if we let the length of the side along the road be \(x\), then the length of the side along the river is \(2x\).
Substituting the given information into the area formula:
\[ 10500 = \frac{1}{2} \times (x + 2x) \times 100 \]
\[ 10500 = \frac{1}{2} \times 3x \times 100 \]
\[ 10500 = 150x \]
Solving for \(x\):
\[ x = \frac{10500}{150} \]
\[ x = 70 \, m \]
So, the length of the side along the road is \(70 \, m\), and the length of the side along the river, which is twice the length of the side along the road, is:
\[ 2x = 2 \times 70 = 140 \, m \]
Therefore, the length of the side along the river is \(140 \, m\).
Step-by-step explanation:
