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If the length of a rectangle is increased by 20% and the width is decreased by 20%, then the area?
- a)decreases by 20%
- b)decreases by 4%
- c)remains the same
- d)increases by 10%
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
If the length of a rectangle is increased by 20% and the width is dec...
Problem Analysis:
Let's assume the original length of the rectangle is L and the original width is W.
According to the problem, the length is increased by 20%, which means the new length is 1.2 times the original length: New Length = 1.2L.
Similarly, the width is decreased by 20%, which means the new width is 0.8 times the original width: New Width = 0.8W.
Solution:
To find the new area of the rectangle, we multiply the new length by the new width:
New Area = New Length * New Width = (1.2L) * (0.8W) = 0.96(LW)
Therefore, the new area is 0.96 times the original area.
Answer Explanation:
The question asks for the change in the area of the rectangle after the changes in the length and width.
Comparing the new area (0.96 times the original area) with the original area, we can see that the new area is 4% less than the original area.
Hence, the correct answer is option B - the area decreases by 4%.
Key Takeaways:
- When the length of a rectangle is increased by a certain percentage and the width is decreased by the same percentage, the area of the rectangle will decrease.
- The decrease in the area is equal to the square of the percentage change in the dimensions. In this case, the decrease is 4%, which is equal to (20% * 20%) = 4%.
Let's assume the original length of the rectangle is L and the original width is W.
According to the problem, the length is increased by 20%, which means the new length is 1.2 times the original length: New Length = 1.2L.
Similarly, the width is decreased by 20%, which means the new width is 0.8 times the original width: New Width = 0.8W.
Solution:
To find the new area of the rectangle, we multiply the new length by the new width:
New Area = New Length * New Width = (1.2L) * (0.8W) = 0.96(LW)
Therefore, the new area is 0.96 times the original area.
Answer Explanation:
The question asks for the change in the area of the rectangle after the changes in the length and width.
Comparing the new area (0.96 times the original area) with the original area, we can see that the new area is 4% less than the original area.
Hence, the correct answer is option B - the area decreases by 4%.
Key Takeaways:
- When the length of a rectangle is increased by a certain percentage and the width is decreased by the same percentage, the area of the rectangle will decrease.
- The decrease in the area is equal to the square of the percentage change in the dimensions. In this case, the decrease is 4%, which is equal to (20% * 20%) = 4%.
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Community Answer
If the length of a rectangle is increased by 20% and the width is dec...
Applying successive percentage increase formula, we have
Hence. the area decreases by 4%.
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If the length of a rectangle is increased by 20% and the width is decreased by 20%, then the area?a)decreases by 20%b)decreases by 4%c)remains the samed)increases by 10%Correct answer is option 'B'. Can you explain this answer?
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