If the length of a rectangle increases by 10%, by what percent should the…
2022
If the length of a rectangle increases by 10%, by what percent should the breadth decrease to maintain the same area?
- A.
10%
- B.
11%
- C.
9.11%
- D.
11.9%
Attempted by 60 students.
Show answer & explanation
Correct answer: C
Solution:
Let the original length be L and the original breadth be B. The original area is L × B.
After a 10% increase the new length = 1.1L.
Let the new breadth be x × B. To keep area the same: 1.1L × xB = L × B, so 1.1 × x = 1.
Therefore x = 1/1.1 = 10/11 ≈ 0.9090909.
The required percentage decrease in breadth = (1 − x) × 100% = (1 − 10/11) × 100% = (1/11) × 100% = 9 1/11% ≈ 9.0909%.
Final answer: The breadth should decrease by 9 1/11% (approximately 9.09%). If 9.11% appears as a given option, it is a slight rounding variation of the exact value.