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The weight of a rectangle is two thirds its length if the perimeter is 210 m find the dimension of the rectangle?
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The weight of a rectangle is two thirds its length if the perimeter is...
Understanding the Problem
To solve for the dimensions of the rectangle, we know two things:
- The weight (W) of the rectangle is two-thirds of its length (L).
- The perimeter (P) of the rectangle is 210 m.
Formulating the Equations
1. The perimeter of a rectangle is given by the formula:
- P = 2(L + W)
2. We also know that:
- W = (2/3)L
Substituting the Weight
- Substitute W in the perimeter equation:
- P = 2(L + (2/3)L)
Calculating the Perimeter
1. Simplifying the equation:
- P = 2(L + (2/3)L) = 2(L + 0.67L) = 2(1.67L)
- P = 3.34L
2. Setting this equal to the given perimeter:
- 3.34L = 210
Finding the Length
1. Solving for L:
- L = 210 / 3.34
- L ≈ 62.83 m
Finding the Width
1. Now, calculate W using:
- W = (2/3)L
- W = (2/3) * 62.83
- W ≈ 41.89 m
Final Dimensions
- Length (L) ≈ 62.83 m
- Width (W) ≈ 41.89 m
Conclusion
The dimensions of the rectangle are approximately:
- Length: 62.83 meters
- Width: 41.89 meters
This solution provides a clear understanding of how the dimensions were derived using the perimeter and the relationship between length and weight.
To solve for the dimensions of the rectangle, we know two things:
- The weight (W) of the rectangle is two-thirds of its length (L).
- The perimeter (P) of the rectangle is 210 m.
Formulating the Equations
1. The perimeter of a rectangle is given by the formula:
- P = 2(L + W)
2. We also know that:
- W = (2/3)L
Substituting the Weight
- Substitute W in the perimeter equation:
- P = 2(L + (2/3)L)
Calculating the Perimeter
1. Simplifying the equation:
- P = 2(L + (2/3)L) = 2(L + 0.67L) = 2(1.67L)
- P = 3.34L
2. Setting this equal to the given perimeter:
- 3.34L = 210
Finding the Length
1. Solving for L:
- L = 210 / 3.34
- L ≈ 62.83 m
Finding the Width
1. Now, calculate W using:
- W = (2/3)L
- W = (2/3) * 62.83
- W ≈ 41.89 m
Final Dimensions
- Length (L) ≈ 62.83 m
- Width (W) ≈ 41.89 m
Conclusion
The dimensions of the rectangle are approximately:
- Length: 62.83 meters
- Width: 41.89 meters
This solution provides a clear understanding of how the dimensions were derived using the perimeter and the relationship between length and weight.
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The weight of a rectangle is two thirds its length if the perimeter is 210 m find the dimension of the rectangle?
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The weight of a rectangle is two thirds its length if the perimeter is 210 m find the dimension of the rectangle? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The weight of a rectangle is two thirds its length if the perimeter is 210 m find the dimension of the rectangle? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The weight of a rectangle is two thirds its length if the perimeter is 210 m find the dimension of the rectangle?.
The weight of a rectangle is two thirds its length if the perimeter is 210 m find the dimension of the rectangle? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The weight of a rectangle is two thirds its length if the perimeter is 210 m find the dimension of the rectangle? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The weight of a rectangle is two thirds its length if the perimeter is 210 m find the dimension of the rectangle?.
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