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A rectangular plot is half as long again as it broad. The area of the lawn is 2/3 hectares. The length of the plot is?
- a)100 meters
- b)66.66 meters
- c)33 meters
- d)(100/ √ 3 ) meters
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A rectangular plot is half as long again as it broad. The area of the ...
Let breadth = b meters.
then, length = 3b/2 meters
∴ b x 3b/2 = 2/3 X 10000
⇒ b2 = (4 x 10000)/9
⇒ b = ( 2 X 100)/3 m
∴ Length = (3/2) x (2/3) x 100 m
= 100 m
then, length = 3b/2 meters
∴ b x 3b/2 = 2/3 X 10000
⇒ b2 = (4 x 10000)/9
⇒ b = ( 2 X 100)/3 m
∴ Length = (3/2) x (2/3) x 100 m
= 100 m
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Community Answer
A rectangular plot is half as long again as it broad. The area of the ...
Understanding the Problem
The problem states that a rectangular plot is half as long again as it is broad. This means if the width (b) of the plot is denoted as x, then the length (l) can be expressed as:
- Length: l = x + (1/2)x = (3/2)x
The area of the plot is given as 2/3 hectares.
Conversion of Area
To work with more familiar units, we convert hectares to square meters:
- 1 hectare = 10,000 square meters
- Therefore, 2/3 hectares = (2/3) * 10,000 = 6,666.67 square meters
Calculating Area
Now, the area (A) of the rectangle can be calculated using the formula:
- A = length * width
- A = (3/2)x * x = (3/2)x^2
Setting the area equal to the calculated area:
- (3/2)x^2 = 6,666.67
Solving for x
To find x, rearrange the equation:
- x^2 = (6,666.67 * 2) / 3
- x^2 = 4,444.44
- x = sqrt(4,444.44) ≈ 66.67 meters (width)
Now, we find the length:
- l = (3/2) * 66.67 ≈ 100 meters
Conclusion
Thus, the length of the plot is approximately 100 meters, confirming that option A is correct.
The problem states that a rectangular plot is half as long again as it is broad. This means if the width (b) of the plot is denoted as x, then the length (l) can be expressed as:
- Length: l = x + (1/2)x = (3/2)x
The area of the plot is given as 2/3 hectares.
Conversion of Area
To work with more familiar units, we convert hectares to square meters:
- 1 hectare = 10,000 square meters
- Therefore, 2/3 hectares = (2/3) * 10,000 = 6,666.67 square meters
Calculating Area
Now, the area (A) of the rectangle can be calculated using the formula:
- A = length * width
- A = (3/2)x * x = (3/2)x^2
Setting the area equal to the calculated area:
- (3/2)x^2 = 6,666.67
Solving for x
To find x, rearrange the equation:
- x^2 = (6,666.67 * 2) / 3
- x^2 = 4,444.44
- x = sqrt(4,444.44) ≈ 66.67 meters (width)
Now, we find the length:
- l = (3/2) * 66.67 ≈ 100 meters
Conclusion
Thus, the length of the plot is approximately 100 meters, confirming that option A is correct.
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A rectangular plot is half as long again as it broad. The area of the lawn is 2/3 hectares. The length of the plot is?a)100 metersb)66.66 metersc)33 metersd)(100/ √ 3 ) metersCorrect answer is option 'A'. Can you explain this answer? for Bank Exams 2025 is part of Bank Exams preparation. The Question and answers have been prepared according to the Bank Exams exam syllabus. Information about A rectangular plot is half as long again as it broad. The area of the lawn is 2/3 hectares. The length of the plot is?a)100 metersb)66.66 metersc)33 metersd)(100/ √ 3 ) metersCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Bank Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangular plot is half as long again as it broad. The area of the lawn is 2/3 hectares. The length of the plot is?a)100 metersb)66.66 metersc)33 metersd)(100/ √ 3 ) metersCorrect answer is option 'A'. Can you explain this answer?.
A rectangular plot is half as long again as it broad. The area of the lawn is 2/3 hectares. The length of the plot is?a)100 metersb)66.66 metersc)33 metersd)(100/ √ 3 ) metersCorrect answer is option 'A'. Can you explain this answer? for Bank Exams 2025 is part of Bank Exams preparation. The Question and answers have been prepared according to the Bank Exams exam syllabus. Information about A rectangular plot is half as long again as it broad. The area of the lawn is 2/3 hectares. The length of the plot is?a)100 metersb)66.66 metersc)33 metersd)(100/ √ 3 ) metersCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Bank Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangular plot is half as long again as it broad. The area of the lawn is 2/3 hectares. The length of the plot is?a)100 metersb)66.66 metersc)33 metersd)(100/ √ 3 ) metersCorrect answer is option 'A'. Can you explain this answer?.
Solutions for A rectangular plot is half as long again as it broad. The area of the lawn is 2/3 hectares. The length of the plot is?a)100 metersb)66.66 metersc)33 metersd)(100/ √ 3 ) metersCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Bank Exams.
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