Three numbers in a 3:5:6 ratio have squares summing to 280. Find the largest number.
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Answer: C. 12
Explanation
Representing the three numbers as 3x, 5x, and 6x incorporates the given ratio into algebraic square terms. Summing the squared expressions results in seventy times the squared variable equal to two hundred eighty. Dividing by seventy gives four, making the variable two and the largest number equal to twelve. Squaring ratio terms involves raising both the numerical coefficient and the variable factor to the second power. Ratio scaling variables allow complex proportional relationships to be converted into solvable algebraic equations. The largest number in a proportional set corresponds to the highest multiplier applied to the common variable.
Option A corresponds to an intermediate number in the ratio rather than the largest required value. Option B represents an incorrect calculation step that misinterprets the scaling variable value. Option D results from multiplying the ratio incorrectly before solving the sum of squares equation.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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