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Length of a rectangle is increased by 10%, and breadth is decreased by 10%. Find the percent effect in the area.
- a)2% increase
- b)1% decrease
- c)2% decrease
- d)1% increase
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Length of a rectangle is increased by 10%, and breadth is decreased b...
Let length = l
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And breadth = b
Area = lb
After increment, length = l x (100 + 10)/100 = l x 110/100 = l x 11/10
After decrement, breadth = b x (100 - 10)/100 = b x 90/100 = b x 9/10
Area = l x 11/10 x b x 9/10
= 99lb/100 lb
% decrease = (lb - 99lb/100)/lb x 100
= (100lb - 99lb)/100 x 1/lb x 100
= lb/100 x 1/lb x 100
= 1%
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Length of a rectangle is increased by 10%, and breadth is decreased b...
Understanding the Problem
To find the percent effect on the area of a rectangle when its length and breadth are changed, we follow these steps:
Initial Area Calculation
- Let the original length of the rectangle be L.
- Let the original breadth of the rectangle be B.
- The original area (A1) = Length × Breadth = L × B.
Changes in Dimensions
- The length is increased by 10%: New Length = L + 0.1L = 1.1L.
- The breadth is decreased by 10%: New Breadth = B - 0.1B = 0.9B.
New Area Calculation
- The new area (A2) = New Length × New Breadth = (1.1L) × (0.9B) = 0.99LB.
Percent Change in Area
- The original area (A1) = L × B.
- The new area (A2) = 0.99LB.
- To find the change:
Change in Area = A2 - A1 = 0.99LB - LB = -0.01LB.
- Percent change in area = (Change in Area / Original Area) × 100 = (-0.01LB / LB) × 100 = -1%.
Conclusion
Thus, the area decreases by 1%. The correct answer is option 'B', which states there is a 1% decrease in the area.
This result highlights how seemingly small percentage changes in dimensions can significantly affect the overall area, demonstrating the non-linear nature of geometric properties.
To find the percent effect on the area of a rectangle when its length and breadth are changed, we follow these steps:
Initial Area Calculation
- Let the original length of the rectangle be L.
- Let the original breadth of the rectangle be B.
- The original area (A1) = Length × Breadth = L × B.
Changes in Dimensions
- The length is increased by 10%: New Length = L + 0.1L = 1.1L.
- The breadth is decreased by 10%: New Breadth = B - 0.1B = 0.9B.
New Area Calculation
- The new area (A2) = New Length × New Breadth = (1.1L) × (0.9B) = 0.99LB.
Percent Change in Area
- The original area (A1) = L × B.
- The new area (A2) = 0.99LB.
- To find the change:
Change in Area = A2 - A1 = 0.99LB - LB = -0.01LB.
- Percent change in area = (Change in Area / Original Area) × 100 = (-0.01LB / LB) × 100 = -1%.
Conclusion
Thus, the area decreases by 1%. The correct answer is option 'B', which states there is a 1% decrease in the area.
This result highlights how seemingly small percentage changes in dimensions can significantly affect the overall area, demonstrating the non-linear nature of geometric properties.
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Length of a rectangle is increased by 10%, and breadth is decreased by 10%. Find the percent effect in the area.a)2% increaseb)1% decreasec)2% decreased)1% increaseCorrect answer is option 'B'. Can you explain this answer?
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