A rectangular plot's length increases by 25%. To keep the area unchanged, by what percent should the width be altered___________?
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Answer: D. Reduced by 20%
Explanation
Increasing the length of a rectangle by twenty five percent multiplies its length dimension by a factor of five over four. To keep the overall area completely unchanged, the width must be multiplied by the reciprocal factor of four over five. A multiplier of four over five represents a fractional decrease of one fifth, which equals a twenty percent reduction. Inverse proportionality governs dimensions of rectangles when area is held constant. Percentage changes represent proportional increases or decreases relative to an initial baseline value. Multiplying reciprocal factors ensures that product totals remain perfectly constant during adjustments.
Economics and consumer pricing often analyze inverse relationships between product quantities and prices. Geometry applications help designers adjust dimensions without altering spatial coverage requirements. Scaling principles are used across engineering to maintain proportional balance in structural designs. Option A is incorrect because changing the length requires a corresponding adjustment in width. Option B would increase the total area rather than keeping it unchanged. Option C incorrectly increases the width when a reduction is required to balance the area.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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