A rectangle has a 4:3 length-to-breadth ratio and an area of 6912 sq cm. Find the ratio of its breadth to its area.
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Answer: A. 1 : 96
Explanation
Expressing rectangle dimensions algebraically using a four-to-three ratio allows area to be expressed quadratically. Dividing the total area by twelve yields five hundred seventy-six, whose square root gives twenty-four for x. Forming the ratio of breadth seventy-two to area six thousand nine hundred twelve simplifies to one to ninety-six. Rectangle area is computed by multiplying length and breadth variables expressed in standard units of length. Algebraic ratio methods solve complex geometric area problems by introducing a common scaling variable x. Simplifying ratios involves dividing both numerator and denominator by their greatest common divisor.
Option B suggests one to forty-eight which results from an incorrect simplification of the breadth-to-area ratio. Option C suggests one to eighty-four which is an arithmetic calculation error not supported by the dimensions. Option D suggests one to sixty-eight which does not match the simplified ratio of breadth to total area.
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- Mathematics
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- Mathematics
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