A rectangle's length increases by 25% and its breadth drops by 20%. What is the impact on its area?
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Answer: A. Remains same
Explanation
The net percentage change formula correctly accounts for successive changes in rectangle dimensions. Multiplying twenty five by negative twenty and dividing by one hundred yields negative five. Subtracting five from twenty five and then subtracting five results in zero percent change. Geometry principles state that area depends on the product of length and breadth. Successive percentage changes combine additively and multiplicatively rather than simply canceling out linearly. Calculations involving percentage changes use the standard formula a plus b plus ab over one hundred.
Retail businesses use similar calculations when adjusting prices and subsequently offering promotional discounts. Understanding multidimensional scaling helps architects design spaces with constant floor surface areas. Financial analysts apply these mathematical models to portfolio growth under fluctuating market conditions. A five percent decrease fails to account for the cross multiplication term in the formula. A five percent increase ignores the negative impact of the breadth reduction on total area. A ten percent increase represents an incorrect addition of the raw percentage values without scaling.
- Subject
- Mathematics
- Category
- Mathematics
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- —
- Difficulty
- medium
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