Question 43 of 45advanced🔧 ApplyNumerical3 marks

If the length of a rectangle is increased by 10% and the area is unchanged, by what percentage (exactly) does the breadth decrease by?

Correct Answer

Given: Original area = L × B New length = 1.1L (10% increase) Area remains unchanged

Calculation: L × B = 1.1L × New B New B = B/1.1 = (10/11)B Decrease in breadth = (1 - 10/11) × 100 = (1/11) × 100 = 100/11% = 9 1/11%

Answer: Breadth decreases by 100/11% (or 9 1/11%).

Exercise: Figure it Out (Section 5) | Q: 11 | (Page Page 29)
For More Understanding

Explanation

The chapter applies percentage concepts to geometry. When one dimension increases and area stays constant, the other dimension must decrease proportionally.

Solution Steps

  1. Original area = L × B

  2. New length = 1.1L (10% increase)

  3. Area unchanged: L × B = 1.1L × New B

  4. New B = B/1.1 = (10/11)B

  5. Decrease in breadth = (1 - 10/11) × 100 = (1/11) × 100 = 100/11% = 9 1/11%

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