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If the length of a rectangle is increased by 20% and breadth is decreased by 20%,find the change in its area?
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If the length of a rectangle is increased by 20% and breadth is decrea...
Understanding the Problem
When the dimensions of a rectangle change, the area can also change. Here, we are given that the length is increased by 20% and the breadth is decreased by 20%.
Initial Area Calculation
- Let the initial length of the rectangle be L.
- Let the initial breadth of the rectangle be B.
- The initial area (A) is calculated as:
- A = L × B
New Dimensions After Changes
- New Length:
- Increased by 20%: New Length = L + 0.2L = 1.2L
- New Breadth:
- Decreased by 20%: New Breadth = B - 0.2B = 0.8B
New Area Calculation
- The new area (A') is calculated as:
- A' = New Length × New Breadth
- A' = (1.2L) × (0.8B)
Calculating the New Area
- A' = 1.2L × 0.8B
- A' = 0.96LB
Change in Area Calculation
- Initial Area (A):
- A = LB
- New Area (A'):
- A' = 0.96LB
- Change in Area:
- Change = A' - A = 0.96LB - LB
- Change = -0.04LB
Conclusion
- The area of the rectangle has decreased by 4% due to the changes in its dimensions.
- Thus, the final result shows that despite the increase in length, the decrease in breadth leads to an overall reduction in area.
When the dimensions of a rectangle change, the area can also change. Here, we are given that the length is increased by 20% and the breadth is decreased by 20%.
Initial Area Calculation
- Let the initial length of the rectangle be L.
- Let the initial breadth of the rectangle be B.
- The initial area (A) is calculated as:
- A = L × B
New Dimensions After Changes
- New Length:
- Increased by 20%: New Length = L + 0.2L = 1.2L
- New Breadth:
- Decreased by 20%: New Breadth = B - 0.2B = 0.8B
New Area Calculation
- The new area (A') is calculated as:
- A' = New Length × New Breadth
- A' = (1.2L) × (0.8B)
Calculating the New Area
- A' = 1.2L × 0.8B
- A' = 0.96LB
Change in Area Calculation
- Initial Area (A):
- A = LB
- New Area (A'):
- A' = 0.96LB
- Change in Area:
- Change = A' - A = 0.96LB - LB
- Change = -0.04LB
Conclusion
- The area of the rectangle has decreased by 4% due to the changes in its dimensions.
- Thus, the final result shows that despite the increase in length, the decrease in breadth leads to an overall reduction in area.
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If the length of a rectangle is increased by 20% and breadth is decreased by 20%,find the change in its area?
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If the length of a rectangle is increased by 20% and breadth is decreased by 20%,find the change in its area? 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 If the length of a rectangle is increased by 20% and breadth is decreased by 20%,find the change in its area? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the length of a rectangle is increased by 20% and breadth is decreased by 20%,find the change in its area?.
If the length of a rectangle is increased by 20% and breadth is decreased by 20%,find the change in its area? 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 If the length of a rectangle is increased by 20% and breadth is decreased by 20%,find the change in its area? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the length of a rectangle is increased by 20% and breadth is decreased by 20%,find the change in its area?.
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