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The sum of squares of three numbers is 280. If the numbers are in the ratio 3:5:6, find the greatest number.

Correct answer: C. 12

  • A. 8
  • B. 6
  • C. 12
  • D. 18

Explanation

Let the numbers be 3k, 5k and 6k. Their squared sum is (3k)² + (5k)² + (6k)² = 9k² + 25k² + 36k² = 70k², so 70k² = 280 and k² = 4, giving k = 2; the greatest number is 6 × 2 = 12. The likely mistake is option d, 18, from applying an incorrect scale factor to the ratio.

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Ratios compare quantities in the same units, while proportions state that two ratios are equal. Problems cover simplification, division in a given ratio, direct and inverse variation, scale, and missing terms, with attention to the difference between a ratio and a fraction representing part of a whole.

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