A square's area is 4096 sq cm. Find the breadth-to-length ratio of a rectangle whose length is twice the square's side and breadth is 24 cm less than the side.
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Answer: D. None of these
Explanation
The square area of forty-forty-six means its side length is sixty-four centimeters. The rectangle length is twice the square side, giving one hundred twenty-eight centimeters. The rectangle breadth is twenty-four less than the side, giving forty centimeters, resulting in a ratio of five to sixteen. Square dimensions are determined by taking the square root of the given total area value. Rectangle dimensions are derived by applying additive and multiplicative scaling rules to the base side. Ratio simplification involves reducing the breadth and length numbers by their greatest common divisor.
Architects and designers frequently scale rectangular components relative to base square reference modules. Manufacturing specifications require precise dimension ratios to ensure parts meet mechanical tolerances. Checking multiple-choice options carefully prevents confusion when calculated ratios do not match listed distractors. Option A suggests an incorrect ratio resulting from calculation errors in the breadth dimension. Option B reverses the numerator and denominator terms of the simplified breadth-to-length ratio. Option C represents an intermediate calculation step rather than the fully reduced final ratio.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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