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Mohan wants to buy a trapezium shaped field its sides along with the river is parallel to and twice the side along the road if the area of this field is 10500
m square and the perpendicular distance between two parallel sides is 100 m find the length of the side along the river?
m square and the perpendicular distance between two parallel sides is 100 m find the length of the side along the river?
Most Upvoted Answer
Mohan wants to buy a trapezium shaped field its sides along with the r...
Understanding the Problem
To find the length of the side along the river in a trapezium-shaped field, we need to use the formula for the area of a trapezium. The area \( A \) is given by:
\[ A = \frac{1}{2} \times (b_1 + b_2) \times h \]
where \( b_1 \) and \( b_2 \) are the lengths of the two parallel sides and \( h \) is the height (or perpendicular distance) between them.
Given Data
- Area \( A = 10500 \, m^2 \)
- Height \( h = 100 \, m \)
- Let \( b_1 \) be the side along the road.
- Let \( b_2 \) be the side along the river (which is twice the length of \( b_1 \)).
Setting Up the Equation
We know \( b_2 = 2b_1 \). Substituting into the area formula, we get:
\[ 10500 = \frac{1}{2} \times (b_1 + 2b_1) \times 100 \]
Simplifying the equation:
- Combine the terms:
\[ 10500 = \frac{1}{2} \times 3b_1 \times 100 \]
- Calculate:
\[ 10500 = 150b_1 \]
Solving for \( b_1 \)
To find \( b_1 \):
\[ b_1 = \frac{10500}{150} \]
Calculating:
\[ b_1 = 70 \, m \]
Finding \( b_2 \)
Now, substituting back to find \( b_2 \):
\[ b_2 = 2b_1 = 2 \times 70 = 140 \, m \]
Conclusion
The length of the side along the river is:
140 m
To find the length of the side along the river in a trapezium-shaped field, we need to use the formula for the area of a trapezium. The area \( A \) is given by:
\[ A = \frac{1}{2} \times (b_1 + b_2) \times h \]
where \( b_1 \) and \( b_2 \) are the lengths of the two parallel sides and \( h \) is the height (or perpendicular distance) between them.
Given Data
- Area \( A = 10500 \, m^2 \)
- Height \( h = 100 \, m \)
- Let \( b_1 \) be the side along the road.
- Let \( b_2 \) be the side along the river (which is twice the length of \( b_1 \)).
Setting Up the Equation
We know \( b_2 = 2b_1 \). Substituting into the area formula, we get:
\[ 10500 = \frac{1}{2} \times (b_1 + 2b_1) \times 100 \]
Simplifying the equation:
- Combine the terms:
\[ 10500 = \frac{1}{2} \times 3b_1 \times 100 \]
- Calculate:
\[ 10500 = 150b_1 \]
Solving for \( b_1 \)
To find \( b_1 \):
\[ b_1 = \frac{10500}{150} \]
Calculating:
\[ b_1 = 70 \, m \]
Finding \( b_2 \)
Now, substituting back to find \( b_2 \):
\[ b_2 = 2b_1 = 2 \times 70 = 140 \, m \]
Conclusion
The length of the side along the river is:
140 m
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Mohan wants to buy a trapezium shaped field its sides along with the river is parallel to and twice the side along the road if the area of this field is 10500 m square and the perpendicular distance between two parallel sides is 100 m find the length of the side along the river?
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Mohan wants to buy a trapezium shaped field its sides along with the river is parallel to and twice the side along the road if the area of this field is 10500 m square and the perpendicular distance between two parallel sides is 100 m find the length of the side along the river? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Mohan wants to buy a trapezium shaped field its sides along with the river is parallel to and twice the side along the road if the area of this field is 10500 m square and the perpendicular distance between two parallel sides is 100 m find the length of the side along the river? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Mohan wants to buy a trapezium shaped field its sides along with the river is parallel to and twice the side along the road if the area of this field is 10500 m square and the perpendicular distance between two parallel sides is 100 m find the length of the side along the river?.
Mohan wants to buy a trapezium shaped field its sides along with the river is parallel to and twice the side along the road if the area of this field is 10500 m square and the perpendicular distance between two parallel sides is 100 m find the length of the side along the river? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Mohan wants to buy a trapezium shaped field its sides along with the river is parallel to and twice the side along the road if the area of this field is 10500 m square and the perpendicular distance between two parallel sides is 100 m find the length of the side along the river? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Mohan wants to buy a trapezium shaped field its sides along with the river is parallel to and twice the side along the road if the area of this field is 10500 m square and the perpendicular distance between two parallel sides is 100 m find the length of the side along the river?.
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