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CLAT Exam  >  CLAT Questions  >   The length of a square is increased by 15% a... Start Learning for Free
The length of a square is increased by 15% and breadth decreased by 15%. The area of the rectangle so formed
  • a)
    neither increases nor decreases
  • b)
    decreases by 2.25%
  • c)
    increases by 2.25%
  • d)
    decreases by 22.5%
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The length of a square is increased by 15% and breadth decreased by 1...
Let the original length of x and original length be y.
Original area = xy
Now new length = 1.15x New breadth = 0.85y
New area = 0.9775xy
%age change = (0.977xy - xy )/xy x 100 = -2.25% where -ve sign shows that here is a decrease in the area of rectangle so formed.
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Most Upvoted Answer
The length of a square is increased by 15% and breadth decreased by 1...
Explanation:
When the length of a square is increased by 15% and the breadth is decreased by 15%, a rectangle is formed. To determine the change in the area of the rectangle, we need to calculate the new area after the dimensions have been altered.

Calculations:
Let the original side length of the square be 'x'. After the changes, the new length = 1.15x and the new breadth = 0.85x.
Therefore, the new area of the rectangle = (1.15x) * (0.85x) = 0.9775x^2

Comparison:
The original area of the square = x^2
The change in area = New Area - Original Area = 0.9775x^2 - x^2 = -0.0225x^2

Conclusion:
The change in area is negative, indicating a decrease. To calculate the percentage decrease, we divide the change by the original area and multiply by 100:
Percentage decrease = (-0.0225x^2 / x^2) * 100 = -2.25%
Therefore, the area of the rectangle decreases by 2.25% when the length of the square is increased by 15% and the breadth is decreased by 15%.
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The length of a square is increased by 15% and breadth decreased by 15%. The area of the rectangle so formeda)neither increases nor decreasesb)decreases by 2.25%c)increases by 2.25%d)decreases by 22.5%Correct answer is option 'B'. Can you explain this answer?
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