A square's side increases by 25%. By what percentage does its area increase?
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Answer: B. 56.25
Explanation
Increasing a side length by 25 percent scales the linear dimension by a decimal factor of 1.25. Squaring the scale factor of 1.25 yields a new total area factor of exactly 1.5625. Subtracting the original baseline area from the new factor reveals a net percentage increase of 56.25 percent. The area of a square is calculated by multiplying its side length by itself. Percentage increases represent relative growth measured against an original baseline value of one hundred percent. Combined scaling effects in two dimensions are calculated by multiplying individual linear growth factors together.
Option A results from a slight calculation error in the decimal expansion of the squared scaling factor. Option C underestimates the true geometric growth by failing to account for the cross-term increase in two dimensions. Option D uses an incorrect formula that incorrectly subtracts baseline values before applying the square operation.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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