UPSC Exam > UPSC Questions > The sides of a rectangular piece of card are ...
Start Learning for Free
The sides of a rectangular piece of card are each 10 per cent too long for a particular project. By what perce the area too large?
Most Upvoted Answer
The sides of a rectangular piece of card are each 10 per cent too long...
Understanding the Problem
When the sides of a rectangular piece of card are each increased by 10%, the resulting dimensions lead to a larger area than necessary. This can be calculated step-by-step.
Calculating the New Dimensions
- Let the original length be L and the original width be W.
- After a 10% increase, the new dimensions become:
- New Length = L + 0.1L = 1.1L
- New Width = W + 0.1W = 1.1W
Calculating the Original and New Area
- Original Area (A₀) = L × W
- New Area (A₁) = New Length × New Width = (1.1L) × (1.1W) = 1.21L × W
Finding the Area Increase
- The increase in area can be expressed as:
- Increase in Area = A₁ - A₀ = (1.21L × W) - (L × W) = (1.21 - 1) × (L × W) = 0.21 × (L × W)
Calculating the Percentage Increase
- The percentage increase in area is given by:
- Percentage Increase = (Increase in Area / Original Area) × 100
- Percentage Increase = (0.21 × (L × W) / (L × W)) × 100 = 21%
Conclusion
- The area of the rectangular piece of card is 21% too large due to the 10% increase in each dimension. This highlights how proportional increases in dimensions can significantly affect the overall area, emphasizing the importance of precision in measurements for specific projects.
When the sides of a rectangular piece of card are each increased by 10%, the resulting dimensions lead to a larger area than necessary. This can be calculated step-by-step.
Calculating the New Dimensions
- Let the original length be L and the original width be W.
- After a 10% increase, the new dimensions become:
- New Length = L + 0.1L = 1.1L
- New Width = W + 0.1W = 1.1W
Calculating the Original and New Area
- Original Area (A₀) = L × W
- New Area (A₁) = New Length × New Width = (1.1L) × (1.1W) = 1.21L × W
Finding the Area Increase
- The increase in area can be expressed as:
- Increase in Area = A₁ - A₀ = (1.21L × W) - (L × W) = (1.21 - 1) × (L × W) = 0.21 × (L × W)
Calculating the Percentage Increase
- The percentage increase in area is given by:
- Percentage Increase = (Increase in Area / Original Area) × 100
- Percentage Increase = (0.21 × (L × W) / (L × W)) × 100 = 21%
Conclusion
- The area of the rectangular piece of card is 21% too large due to the 10% increase in each dimension. This highlights how proportional increases in dimensions can significantly affect the overall area, emphasizing the importance of precision in measurements for specific projects.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
The sides of a rectangular piece of card are each 10 per cent too long for a particular project. By what perce the area too large?
Question Description
The sides of a rectangular piece of card are each 10 per cent too long for a particular project. By what perce the area too large? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The sides of a rectangular piece of card are each 10 per cent too long for a particular project. By what perce the area too large? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sides of a rectangular piece of card are each 10 per cent too long for a particular project. By what perce the area too large?.
The sides of a rectangular piece of card are each 10 per cent too long for a particular project. By what perce the area too large? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The sides of a rectangular piece of card are each 10 per cent too long for a particular project. By what perce the area too large? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sides of a rectangular piece of card are each 10 per cent too long for a particular project. By what perce the area too large?.
Solutions for The sides of a rectangular piece of card are each 10 per cent too long for a particular project. By what perce the area too large? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of The sides of a rectangular piece of card are each 10 per cent too long for a particular project. By what perce the area too large? defined & explained in the simplest way possible. Besides giving the explanation of
The sides of a rectangular piece of card are each 10 per cent too long for a particular project. By what perce the area too large?, a detailed solution for The sides of a rectangular piece of card are each 10 per cent too long for a particular project. By what perce the area too large? has been provided alongside types of The sides of a rectangular piece of card are each 10 per cent too long for a particular project. By what perce the area too large? theory, EduRev gives you an
ample number of questions to practice The sides of a rectangular piece of card are each 10 per cent too long for a particular project. By what perce the area too large? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup