A square's length and breadth are increased by 40% and 30% respectively. By what percentage does the new rectangle exceed the square's area:________?
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Answer: C. 82%
Explanation
Percentage increases in length and breadth affect the overall area of a two dimensional shape. Applying successive percentage change formulas combines the dimensional increases into a single metric. The net percentage increase in area evaluates correctly to eighty two percent. When two dimensions scale independently, the net area change follows a multiplicative percentage formula. Successive percentage increases are calculated using the standard net change formula for products. Percentage calculations are unitless, making them universally applicable to any initial square size.
Economic analysis uses percentage scaling to track inflation and market growth over time. Land development projects evaluate area expansion when property dimensions are increased. Understanding successive percentage changes prevents common errors in financial and geometric calculations. Option a suggests forty two percent which underestimates the combined multiplicative area growth. Option b proposes sixty two percent which results from incorrectly adding instead of compounding percentages. Option d is incorrect because the correct percentage increase can be determined definitively.
- Subject
- Mathematics
- Category
- Mathematics
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- —
- Difficulty
- medium
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