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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?
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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.
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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?
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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?.
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